By Elizabeth Cohen and Katherine Grise, CNN

(CNN) -- When he was 11 years old, LJ Stroud of St. Augustine, Florida, had a tooth emerge in a place where no tooth belongs: the roof of his mouth.

LJ was born with severe cleft lip and palate, which explained the strange eruption, as well as the constant ear infections that no antibiotic could remedy.

With her son in terrible pain, Meredith Stroud arranged for surgeries to fix his problems.

But just days before the procedures were to take place, the surgeons' office called to cancel them.

Like nearly half of all children in Florida, LJ is on Medicaid, which has several types of insurance plans. The state had switched LJ to a new plan, and his surgeons didn't take it.

LJ wasn't alone. In the spring and summer of 2015, the state switched more than 13,000 children out of a highly respected program called Children's Medical Services, or CMS, a part of Florida Medicaid. Children on this plan have serious health problems including birth defects, heart disease, diabetes and blindness.

The state moved the children to other Medicaid insurance plans that don't specialize in caring for very sick children.

Stroud says that for her son, the consequences were devastating. Despite hours of phone calls, she says, she couldn't find surgeons on his new insurance plan willing to do the highly specialized procedures he needed. Over the next seven months, her son lost 10 pounds, quit the football team and often missed school.

"He was in pain every day," Stroud said. "I just felt so helpless. It's such a horrible feeling where you can't help your kid."

LJ filed a lawsuit against the state of Florida, and he was eventually placed back on Children's Medical Services and received the care he needed. But some Florida pediatricians worry about other children with special health care needs who, two years later, are still off the program.

The doctors aren't just worried; they're angry.

First, the data analysis the state used to justify switching the children is "inaccurate" and "bizarre," according to the researcher who wrote the software used in that analysis.

Second, the screening tool the state used to select which children would be kicked off the program has been called "completely invalid" and "a perversion of science" by top experts in children with special health care needs.

Third, in fall 2015, a state administrative law judge ruled that the Department of Health should stop using the screening tool because it was unlawful. However, even after the judge issued his decision, the department didn't automatically re-enroll the children or even reach out to the families directly to let them know that re-enrollment was a possibility.

Finally, parents and Florida pediatricians raise questions about the true reasons why Florida's Republican administration switched the children's health plans. They question whether it was to financially reward insurance companies that had donated millions of dollars to the Republican Party of Florida.

"This was a way for the politicians to repay the entities that had contributed to their political campaigns and their political success, and it's the children who suffered," said Dr. Louis St. Petery, former executive vice president of the Florida chapter of the American Academy of Pediatrics.

Experts outside Florida are also disturbed that the children were switched out of CMS, a program that's served as a model for other states for more than 40 years.

"CMS is well-known and well-respected," said Dr. James Perrin, professor of pediatrics at Harvard Medical School. "It's one of the earlier programs to build in assurances that these kids get the kind of care they need."

"These are the sickest and most vulnerable kids, and (changing their insurance) can mean life or death for them," said Joan Alker, executive director of the Center for Children and Families at Georgetown University. "This is really very troubling."

Dr. Rishi Agrawal, an associate professor of pediatrics at Northwestern University's Feinberg School of Medicine, agreed, adding that Florida should have more carefully considered how the insurance switch would affect the children's health care.

"The process in Florida was particularly abrupt and poorly executed," he said.

Mara Gambineri, a spokeswoman for the Florida Department of Health, said that "at no time (during the insurance switch) did children go without medically necessary services."

State officials, including a spokesman for Governor Rick Scott's office, initially declined to comment directly on the pediatricians' and parents' concerns that the children might have been switched to benefit contributors to the Republican Party of Florida. On Friday, after this story was published, the Florida Department of Health released a statement asserting that such a claim "is 100 percent false."

"The department's number one priority is protecting the health and well-being of all Florida residents, especially children with special health care needs," Gambineri wrote in an earlier email. "The department remains committed to providing quality health care services to Florida's children with special health care needs."

A mother's anguish

In spring 2015, LJ's mother received a phone call from a nurse at the Florida Department of Health.

Stroud had no idea that one word she would say to that nurse -- just one single word -- would cause her son months of pain and suffering.

The nurse asked Stroud a series of questions, including whether LJ was limited in his ability to do things other children could do.

Despite his birth defect, LJ goes to school and plays with friends, so she answered no.

Stroud says that because of that answer, LJ lost his insurance with CMS, the program that has cared for children with special health care needs in Florida for 40 years, and was put on a different Medicaid insurance plan.

LJ was one of 13,074 Florida children kicked off CMS -- that's about one in five children in the program -- as a result of the telephone survey, according to a presentation, testimony and a letter from Florida's top health officials.

Stroud thinks back to her answer to the nurse's question about limitations.

"That question's not fair," Stroud said of the one that got her child kicked off CMS. "What [the Florida Department of Health] did was totally wrong."

"It was a trick question," she added.

Pediatrician: 'A truly duplicitous question'

Experts agree with her.

"I personally find it pretty astonishing that they can take a survey question like that and use it to justify the de-enrolling of these kids," said Dr. Jay Berry, an assistant professor of pediatrics at Harvard Medical School who studies policies for children with special health care needs.

What Florida did was "completely invalid," added Dr. John Neff, professor emeritus of pediatrics at the University of Washington, another expert on children with special health care needs.

The pediatricians explained that many children with serious and chronic medical conditions -- such as cleft lip and palate, HIV, diabetes and cystic fibrosis -- are often able to do things other children can do. However, they still require extensive and highly specialized medical care.

The question the Florida Department of Health nurses asked -- "Is your child limited or prevented in any way in his or her ability to do the things most children of the same age can do?" -- would lead to disqualifying children who truly have special medical needs from a program designed for them, said Stephen Blumberg, associate director for science at the National Center for Health Statistics and one of the world's leading experts on the epidemiology of children with special health care needs.

"You would get false negatives. Your conclusion would be that a child does not have special health care needs when, in fact, the child does," he added.

The Department of Health no longer uses the same screening method that resulted in 13,074 children being removed from CMS.

"It is unfortunate the negativity surrounding this issue is a continued topic of inquiry, as the department and our stakeholders have put in a significant amount of time and effort to move past this issue for the benefit of the children we serve," wrote Gambineri, the Department of Health spokeswoman.

But pediatricians in Florida point out that many children who were removed from Children's Medical Services using the controversial questionnaire were never put back on.

"This was a truly duplicitous question," said Dr. Philip Colaizzo, a pediatrician in Jupiter, Florida, who said that many of his patients with special health care needs were taken off CMS. "It was a trick question."

"It's a perversion of science," said Dr. Jeffrey Goldhagen, professor of pediatrics at the University of Florida College of Medicine and medical director of the Bower Lyman Center for Medically Complex Children at Wolfson Children's Hospital.

Goldhagen added that he was speaking for himself and not the institutions where he works.

"It was a scam job," added Dr. Nancy Wright, a pediatric endocrinologist in Tallahassee who said that dozens of her patients with diabetes were removed from the program.

"They really tried their darnedest to kick the kids out of CMS," added Dr. Carrol Fenn, an orthodontist in West Palm Beach. "They've messed up kids' lives."

"They're the most vulnerable of our population, and that they can be booted off the plan that was designed to help them is just amazing. How can someone in an office make a decision like that?" asked Dr. John Obi, an adjunct clinical professor in plastic surgery at the University of Florida, who operates on children with cleft lip and palate.

"I congratulate whoever came up with that question," he added wryly. "If you want to exclude virtually anybody, that's the way to do it."

Johns Hopkins expert: 'I'm speechless'

Christina Bethell's team came up with that question -- and she's furious.

Bethell is a professor at the Johns Hopkins Bloomberg School of Public Health. She and her team spent many years and millions of dollars coming up with the right questions to accurately identify children across the United States who might have special health care needs.

The list of questions -- known as the Children with Special Health Care Needs Screener -- is publicly available on the Hopkins website. Many state and federal agencies use it to help decide which children might benefit from special health services.

The Florida Department of Health, however, used the questions to do something completely different: to kick children out of a program.

That's scientifically invalid, Bethell said. Using the questions that way -- especially the question about limitations -- would lead to denying children with special health care needs the services they require.

"I'm speechless," she said.

To make matters worse, Bethell said, Florida repeatedly and publicly cited research done by her group at Hopkins -- the Children and Adolescent Health Measurement Initiative -- to support the children's removal from CMS.

"I feel really manipulated," she said.

She thinks of the children who were taken off CMS and fumes that the tool used to remove them was her own work.

"I'm angry," she said. "And I'm crestfallen for these families."

Grave consequences for Florida children

The Shabanehs in Tallahassee are one of those families.

Aref Shabaneh, 8, is blind, and his sister, Yasmeen, 11, is severely visually impaired. Their mother, Reema Shabaneh, says they were kicked off CMS in 2015.

Shabaneh says she told the Florida Department of Health nurse that they didn't have limitations.

"Aref wants to do everything by himself," she said. "He can play ball with friends. The ball has a bell, so he can hear it coming."

After they were kicked off CMS, Shabaneh said, she couldn't find an ophthalmologist on the new insurance plan willing to care for her children.

"I was so scared," she said.

When Jennifer Rodriguez received the phone call from the Department of Health nurse, she said, she told the nurse she didn't know how to answer the question about limitations. Her son, Alejandro, suffers from a congenital heart defect, asthma and kidney problems. Sometimes, his heart races and he has trouble breathing, but other times, he feels up to playing soccer with his friends.

"When I tried to explain the answer, she cut me off and said she was just doing her job and needed a yes or a no," she said.

Rodriguez says she answered that her son, who was 10 at the time, did not have limitations. He then lost his CMS coverage.

"It makes me angry, because you would think that since he's seeing a cardiologist, a nephrologist, a urologist and an asthma doctor, they would see he's not your average child," she said.

LJ, Alejandro and the Shabaneh children filed lawsuits and were put back on CMS. They were represented by the Public Interest Law Center at Florida State University.

Many Florida pediatricians say their patients also suffered when they were taken off CMS and put on other Medicaid plans. The doctors say those other plans typically have fewer pediatric specialists than CMS, which specializes in caring for very sick children.

Dr. Lisa Cosgrove, a pediatrician in Merritt Island, Florida, said she had a difficult time finding an orthopedist to treat a 6-year-old with a broken elbow who had been taken off CMS. The girl ended up having surgery later than she should have and now can't extend her elbow all the way.

She said a baby born with a clubfoot also suffered because she couldn't find an orthopedist willing to take the baby's plan. The baby couldn't have the necessary casts to twist the foot back into place and may need surgery, Cosgrove said.

Dr. Elizabeth Curry, a pediatrician in Port St. Joe, Florida, said that last year, she took care of a baby whose eye wiggled back and forth involuntarily, which can be a sign of a brain tumor.

Curry said it took her more than a month to find an ophthalmologist willing to take the baby's Medicaid plan -- and the doctor she finally found was three hours away, in Pensacola.

Fortunately, the baby turned out to be fine.

"This child could have had cancer. That's a kid who should have seen a doctor right away," Curry said. "I feel terrible for these children. It makes me so angry."

Because of problems like these, switching the children's insurance "was a complete dereliction of Florida's responsibility to children," said Goldhagen, the professor of pediatrics at the University of Florida College of Medicine.

Gambineri, the spokeswoman for the Florida Department of Health, said the children didn't suffer as a result of the switch, because the insurance plans they were moved to were "more than capable" of caring for them. She added that even before the 13,074 children were switched, those plans cared for tens of thousands of children with special health needs.

Other pediatricians agree that plans besides CMS have done a good job of caring for these very sick children.

The other plans "do a pretty good job with our families," said Dr. Karalee Kulek-Luzey, medical director of the Pediatric Health Care Alliance, a group practice with multiple locations in the Tampa area. "They're working really hard."

"For the most part, they do a good job," said Dr. Michael Freimark, a pediatrician in Plantation, Florida.

"We have a good relationship with the plans," said Dr. Michael Gervasi, president and chief executive officer of the Florida Community Health Centers, a large medical practice with offices in several counties. Most of the time, he said, the plans take care of the children's needs, but if there's ever a problem, his practice contacts the plan, and they fix it.

Florida's 'outreach' to experts

In January 2016, about eight months after the Florida Department of Health started to move the 13,074 children out of CMS, Jennifer Tschetter, then the department's chief operating officer, testified before the state legislature. She said that the decision to use the Hopkins screening tool was made "in consultation with ... national experts."

But it remains unclear who those experts were.

Tschetter, who has since left state government, did not respond to phone calls and emails seeking comment.

Gambineri, the Florida health department spokeswoman, said the department did "research" into what Louisiana, California, Texas and New York "were doing and experiences they had in regard to clinical eligibility for children with special health care needs."

When asked for the names of individuals Florida consulted in those states, Gambineri didn't respond.

Gambineri added that "outreach" was made to the federal Health Resources and Services Administration.

An official at that agency said she spoke with a Florida health official.

Dr. Marie Mann, senior medical adviser in the Division of Services for Children with Special Health Needs at the federal agency's Maternal and Child Health Bureau, said she spoke with Kelli Stannard, then interim chief, bureau of network operations, at CMS.

Mann says she told Stannard she couldn't give her any guidance.

"I told her I was not in a position to provide advice," Mann said.

Mann said she suggested that Florida health officials reach out to Daniel Armstrong and Dr. Jeffrey Brosco, director and associate director respectively of the Mailman Center for Child Development at the University of Miami Miller School of Medicine.

"We will make sure they're both involved in this review process," Stannard wrote back to Mann in an email obtained by CNN under the Freedom of Information Act.

CNN asked Gambineri, the department spokeswoman, whether the department ever reached out to Armstrong to review and make recommendations on using the telephone survey to screen children out of CMS.

"Not to our knowledge," Gambineri answered.

"I played no role in the decision-making process related to the use of the tool for the Children's Medical Services program," Armstrong wrote in an email to CNN.

Brosco said he told the Department of Health that in his opinion, a child should not be kicked off CMS based on a parent's answer to the question about the child's limitations.

"I gave them my feedback, and they said, 'thank you for your work,' " Brosco said.

In July, Brosco was named the Florida Department of Health's deputy secretary for CMS.

Christmas shopping at the Florida Mall

Despite the lack of support from the very experts they'd consulted, Florida health officials forged ahead with using the phone survey to disqualify children from CMS.

They had a schedule to stick to.

In November 2014, state officials set out to "go live" with the phone survey in six months, according to a timeline developed by the state and obtained by CNN under the Freedom of Information Act.

Before implementing the surveys, the officials gave themselves 21 days to "solicit feedback from the field" about the questions they would ask the parents.

One of the first things they did was to ask one of the state's most experienced pediatricians to leave a meeting.

It was St. Petery, who at the time was the executive vice president of the Florida chapter of the American Academy of Pediatrics and who has an encyclopedic knowledge of Medicaid rules and regulations. He'd served as interim director of CMS for six months during the mid-1970s.

He'd also been a thorn in the side of the state Department of Health for years. He'd been instrumental in a lawsuit that accused the state of failing to reimburse doctors properly in the Medicaid program and to ensure that children receive adequate care.

His side eventually won that lawsuit, and the American Academy of Pediatrics gave him a prestigious award for being "a tireless advocate for children's health and well-being."

On December 13, 2014, St. Petery showed up at the Department of Health meeting. It was for the regional medical directors of CMS, the group of pediatricians who help run the program. St. Petery wasn't one of the directors, but he'd been attending their meetings for many years in his role with the Florida chapter of the American Academy of Pediatrics.

St. Petery said that just before the meeting started, Tschetter, then the department's chief operating officer, approached him.

"She said, didn't I want to go Christmas shopping at the Florida Mall?" St. Petery remembered. The mall was adjacent to the conference center in Orlando where the meeting was taking place.

St. Petery said he told Tschetter that he hates shopping, especially around the holidays, and wanted to stay at the meeting.

"I protested. I asked her, is this meeting not in the sunshine?" he said, referring to Florida's Sunshine Law, which gives the public the right to access most government meetings.

"After she told me for the third time to leave, I decided not to create a scene," he said.

St. Petery got up and left.

Other doctors watched the action, stunned.

"We were all kind of shaking," said Dr. Barbara Rumberger, one of the CMS regional medical directors who attended the meeting.

After St. Petery departed, health officials explained that they would start screening children off of CMS. Their justification: a new analysis showing that half the children on CMS might not belong there.

There are no minutes for this meeting, according to Department of Health officials, but a year later, Tschetter presented similar data to the Florida Legislature.

A 'totally inaccurate' analysis

By Florida law, a child can be in CMS only if he or she has a "chronic and serious" condition requiring health care "of a type or amount beyond that which is generally required by children."

The analysis Tschetter presented showed that about half of the children on CMS had lower than average risk scores, an assessment of how much a patient uses health care services.

Tschetter called these results "surprising." By legislative mandate, children on CMS are supposed to have health needs greater those of other children.

"The analysis made clear, certainly to the department, that we were not meeting legislative direction: (that) the children in the plan have both chronic and serious health care conditions," Tschetter told legislators. "It was clear to the department that something had to be done, because complying with legislative direction is certainly not optional."

But an expert who developed the software Florida used to make that data analysis said the state did its calculations incorrectly.

"It's totally inaccurate," said Todd Gilmer, co-developer of the Chronic Illness and Disability Payment System and chief of the division of health policy at the University of California, San Diego.

Gilmer's software, which is used by dozens of state Medicaid programs, tracks patients' diagnoses and their prescription drug use to calculate risk scores for each individual.

After viewing Florida officials' analysis of the data, he said they made two errors when they calculated that half the children on CMS had below-average risk scores.

First, he explained that his software relies on doctors' diagnoses, and Florida failed to account for the fact that doctors frequently don't document a child's full diagnosis in the medical record. For example, if a quadriplegic child goes to the doctor because of bedsores, doctors often write down the reason the child came in -- the bedsores -- instead of the more serious diagnosis of quadriplegia.

Second, he said, Florida did the wrong calculation for disabled children, who represent 40% of the patients on CMS, according to Mallory McManus, a spokeswoman for Florida's Agency for Health Care Administration.

He said his software compares disabled children with each other. Even the ones who fall in the lower half of the risk-score spectrum still have serious and chronic illnesses, he said, such as HIV or heart failure.

He said that what Florida did was akin to assembling a group of people who are over 7 feet tall and calling the bottom half of that group short.

Gilmer called Florida's analysis "kind of bizarre" and said he was disappointed to see his software "misapplied" by the Florida Department of Health.

Spokeswomen for the Florida Department of Health and the Agency for Health Care Administration did not respond directly to Gilmer's criticism.

Gambineri, the health department spokeswoman, said that the department no longer uses the screening method that it used in 2015 and that parents can ask to have their children re-screened at any time.

"Our mission is now and has always been to provide the best health care possible to the populations that we serve," McManus wrote in an email.

Pediatrician: 'We were just irrelevant'

Pediatricians say that by the time the Department of Health meeting was held at the Orlando conference center at the end of 2014, they felt like Florida was dead-set on screening a large number of children off CMS.

They said state officials didn't listen to their concerns, even though they were stated repeatedly, both in person and in writing.

At the meeting, health officials asked the pediatricians to tell them what was on their minds, according to Rumberger, one of the doctors who was there.

She said she and her colleagues brought up concerns that children might be taken off CMS inappropriately.

The Department of Health official wrote down what the doctors said on pieces of paper taped to the wall, Rumberger said. The official then told the doctors that these were issues to discuss at another time.

"She said, 'We're going to park these. We're putting these ideas in the parking lot for some time, and we're not talking about these things today,' " Rumberger remembered, adding that she was speaking on behalf of herself and not in her role as a CMS regional medical director.

"We were all amazed at what they did," she added.

A few months later, the state held a series of telephone conference calls with the same CMS regional medical directors.

"They didn't ask us 'What do you think?' or 'Do you have any suggestions?' " Rumberger said. "It was just 'This is how we're going to do it.' It was clear they didn't want to have a free discussion."

"It appears to be a very conscious decision to not get input and not receive any dissension," said Goldhagen, the professor of pediatrics at the University of Florida. "We were just irrelevant."

Dr. Rex Northup, another CMS regional medical director and associate professor of pediatrics at the University of Florida College of Medicine, agrees.

"It was like, 'When we want your opinion on a given topic, we'll let you know, and we'll provide that opinion to you,' " Northup said, adding that he speaks for himself and not the university or any other institution.

Several doctors present on those conference calls said they voiced their concerns anyway.

There's no record of these concerns. According to the Florida Department of Health, no minutes were taken of these phone conferences.

CNN asked the Florida Department of Health about the meeting where St. Petery was asked to leave and about doctors' complaints that the state steamrolled through a screening tool that would harm sick children.

"When CMS began the process of implementing a new screening tool in 2014, the department may have underestimated the need for stakeholder input and the time required to obtain feedback and ensure our community was comfortable with the mechanisms for determining clinical eligibility," responded Gambineri, the Department of Health spokeswoman.

She added that the department has "engaged our stakeholders using several methods" including public meetings to solicit input from patients, parents and providers and "remains open to feedback and input in order to best serve children with serious and chronic medical conditions."

True to its schedule, the state started screening children off CMS in May 2015.

Florida pediatricians repeatedly told the state that it was hurting sick, vulnerable children.

In August 2015, Goldhagen, Rumberger, Northup and 11 other doctors with positions at CMS wrote a letter to a Department of Health official saying the screening process was "flawed" and was removing too many children.

The doctors did not receive a response, Goldhagen said.

Two months later, St. Petery wrote to Department of Health officials, sharply criticizing the use of the screening tool.

He said he never received a response, either.

Curry, the Port Saint Joe pediatrician who practices in a rural area of the Florida Panhandle, said she also complained to the state's Agency for Health Care Administration about children being kicked off CMS, along with other issues affecting children on Medicaid.

She said the agency worked with her on some of the other issues but didn't respond to her complaints about the children being taken off CMS.

"Our Agency has been in contact with the provider and is working with the health plan to resolve what issues might be resolved," wrote McManus, the agency spokeswoman.

Curry said she took her complaints even higher.

"I even called the governor's office once and left a message," she said. "I admit that I finally gave up. I'm just trying to take care of my patients."

Pediatricians interviewed for this story said they felt pressure from the state not to speak to the media about the removal of the children from CMS.

On November 15, 2016, Dr. John Curran, then the Florida Department of Health's deputy secretary for CMS, said on a conference call that a CNN reporter was working on this story, according to several doctors on the call.

That evening, a department official wrote an email to the doctors who'd been on the call. It advised these pediatricians that prior to responding to media inquiries, they should contact the department's communications director.

"I'm going to be so fired for saying all these things," Rumberger said.

But she and other pediatricians say they're speaking up because they feel that the Department of Health hurt children because they didn't listen to their concerns.

They say it could be because pediatricians don't tend to have millions of dollars to donate to political campaigns.

But insurance companies do.

'Like a plot in a Carl Hiaasen novel'

All of this -- the telephone survey, the question about limitations, the analysis that's been called flawed -- leaves many Florida parents and pediatricians suspicious about why the state wanted to take 13,074 children off CMS and why it worked so hard and so quickly to do it.

Switching the children from CMS to the other Medicaid plans didn't save taxpayers money, according to McManus, the agency spokeswoman.

The doctors wonder, then, whether the inspiration for the change was political: to send taxpayers' dollars to generous donors to the Florida Republican Party.

CMS is a public program; it's not owned by a private insurance company.

When the children were taken off CMS, they were switched to 11 insurance plans that are owned by private companies. The parent companies of nine of those 11 plans donated a total of more than $8 million to Florida Republican Party committees in the five years before the children were switched.

"I knew it had to be about money," said Wright, the pediatric endocrinologist in Tallahassee who said that dozens of her patients had their insurance switched. "This sounds very believable for Florida, and I'm from Florida."

"When this was all unfolding, I told my office manager, 'I feel like we're in a plot in a Carl Hiaasen novel,' " she added, referring to the Miami Herald columnist who writes about politics and corruption in Florida.

The companies that own the nine insurance plans contributed $8.6 million to Florida Republican Party committees from 2010 to 2014, according to an analysis done for CNN by the National Institute on Money in State Politics, a nonpartisan nonprofit group.

Here's a breakdown of how much money each insurance company with a Medicaid contract contributed to Florida Republican Party committees from 2010 to 2014:

$5.9 million from Blue Cross and Blue Shield of Florida. Florida True Health is an affiliate of Blue Cross and Blue Shield of Florida. At the time the money was contributed, Florida True Health owned 40% of Prestige Health Choice, which has a Medicaid contract with the state of Florida. In 2015, Florida True Health purchased Prestige outright.

Contributions between $232,500 and $668,082 from each of six insurance plans and their parent companies that have contracts with Florida Medicaid: Amerigroup, UnitedHealthcare of Florida, Humana, Sunshine State Health Plan, Aetna and WellCare. WellCare's Florida Medicaid policy is marketed under the name Staywell.

$90,000 from Simply Health, which owns a Medicaid plan called Better Health.

$849,433 from Miguel Fernandez, the former chairman of Simply Health. In addition, Fernandez donated about $1.3 million to Scott's Let's Get to Work political action committee from 2010 to 2014.

Insurance companies' outsize contributions to Florida Republicans

Nearly all states pay insurance companies to insure some of their Medicaid patients; this is not unique to Florida.

And insurance companies often contribute money to state political parties. That's not unique to Florida, either.

What is unusual is the size of the contributions, even for a large state.

Take UnitedHealthcare, an insurance giant with business in all 50 states. From 2010 to 2014, United contributed $442,500 to Florida Republican Party committees, according to the National Institute on Money in State Politics.

The company's next largest contribution to any other state political party was $145,000 to California Democrats -- less than half the Florida amount.

Humana, another insurance company with a national reach, gave substantially more money to Florida Republican Party committees than to any other state political party committees.

From 2010 to 2014, Humana donated $482,815 to Florida Republican Party committees. Its next largest contribution was $213,823 to Florida Democrats. The next largest contribution after that was $22,000 to the Illinois GOP, less than one-20th the size of the contribution to Florida Republicans.

Blue Cross and Blue Shield of Florida gave Florida Republican Party committees $5.9 million from 2010 to 2014 and gave Florida Democrats $1.8 million. The next largest contribution after that from any other Blue Cross and Blue Shield company in the United States was $730,696 from Blue Shield of California to Democrats in that state -- about one-eighth the size of the contribution to Florida Republicans.

Florida's payments to the insurance companies

Nearly all states pay private insurance companies monthly premiums to insure Medicaid patients. It's become big business.

The Florida Department of Health declined to say how much it paid the private insurance companies to insure the 13,074 children when they were switched out of CMS.

"If they got 13,000 new kids, (it's) that times however many dollars per member per month," St. Petery said. "I think that's a lot of money when you start talking about that many kids."

These children came from CMS, a Medicaid program for sick children, and the state pays insurance companies more money to care for such children.

This is how it works, according to McManus, the spokeswoman for the Florida Agency for Health Care Administration.

Florida takes a look at all the people who've signed up with an insurance company and calculates a risk score for that group based on factors such as the age of the enrollees in the plan and their health conditions.

A plan with the lowest risk score has a "typical population" and might be paid a rate of, for example, $320 per person per month, McManus said. A plan with sicker enrollees might have a risk score that's twice as high and so would be paid $640 per person per month, she added.

The numbers can get even higher from there.

"The state will pay a pretty good rate for these children," said Agrawal, the pediatrician at Northwestern who studies health care systems for children with special medical needs.

"They could get paid thousands more per month for a child with serious medical needs," said Steve Schramm, founder and managing director of Optumas, a health care consulting group.

"The enhanced reimbursement may be 10 times what the insurance companies get for a well child," said Goldhagen, former director of Florida's Duval County Health Department.

Sick children are, of course, also costlier for insurance companies because they need more care. But insurance plans monitor that care to manage costs.

"Plans have gotten very sophisticated in their ability to manage very sick kids, so their willingness to take very sick kids is great," said Jeff Myers, president and CEO of Medicaid Health Plans of America, an industry group representing insurance companies.

Pediatricians questioned whether such outsize political donations were an attempt to gain influence and favor with Florida's Republican administration, which orchestrated the transfer of the children out of CMS and to the private companies.

"It certainly raises a lot of suspicion and concern," said Northup, the associate professor at the University of Florida College of Medicine.

"Why would they make contributions in the hundreds of thousands and the millions to Florida Republicans? Why would they be so uniquely committed to Republicans in Florida? It gives one pause," he added. "If you follow the money, at the very least, it's worrisome."

"It's the left-hand-washing-the-right-hand kind of business," said Dr. Joseph Chiaro, who was Florida's deputy secretary of health from 2005 to 2011. "It breaks my heart."

Six Florida pediatricians gathered in Orlando to tell CNN their concerns. They practice in rural, suburban and urban areas. Some of them are Republicans, and others are Democrats.

They said they feared that big donors had influence on the state's decision-making process and that in many cases, the children suffered as a result.

"I don't see this in writing anywhere, but my impression is, this was a way for political payback at the expense of the sickest of the Medicaid children," St. Petery said.

"It just comes back to money or power. It's not about health care for the children," said Wright, the pediatric endocrinologist in Tallahassee.

"Just follow the money," said Colaizzo, who runs a rural health care clinic in Pahokee, Florida.

State leaders "don't give a damn about the kids. They don't give a damn about the families," said Dr. Marcy Howard, a pediatrician in Crystal River, Florida.

State officials and insurance companies respond

McManus, the spokeswoman for the Florida Agency for Health Care Administration, wrote in an email."The Statewide Medicaid Managed Care program was designed to provide comprehensive care to recipients through high quality health plans with a payment structure designed to ensure that plans paid an appropriate rate based on the health conditions of those enrolled in their plan."

"The program currently covers more than 2 million of Florida's children, offers the strongest provider network and access standards in program history, and provides families with a choice of high quality, nationally accredited plans so that they can choose the plan that best suits their needs, including specialty plans for those who qualify," she added.

CNN reached out to officials at all nine insurance companies. Two responded.

"WellCare contributes to a variety of organizations that shape health care policy, including the Florida Republican Party committees, the Democratic Party committees and those without political affiliation," wrote Alissa Lawver, a spokeswoman for WellCare. "The company also discloses and publicly reports all political contributions on its website above and beyond the requirements of state and federal law. As a provider of managed care, WellCare is committed to partnering with the state of Florida to provide access to quality, affordable health care solutions for the state's most vulnerable populations. We maintain a robust provider network and offer comprehensive care management services to create personalized, coordinated care plans to help improve and maintain the health of families and children across the state."

She added that WellCare has accountability to Florida's Agency for Health Care Administration, "which provides careful oversight of the state's Medicaid program to ensure all members, including children that transitioned from Children's Medical Services, receive access to the right care, at the right time and in the most appropriate setting."

Ethan Slavin, a spokesman for Aetna, said the company makes "donations to campaigns for both major political parties to support and address issues that impact our customers and members."

He added that "we are required to meet state rules and regulations regarding our network of health care providers and are consistently compliant with those requirements" and that "we regularly work with our members, health care providers and the state of Florida to move children with special health care needs into the Children's Medical Services program, when appropriate and in the best interest of our members. Our integrated care management program regularly identifies these children and assists in this process."

Miguel "Mike" Fernandez, founder and former chairman of Better Health, said he had contributed several million dollars to both Republicans and Democrats. He added that states move Medicaid patients into the care of private companies so they can "move the risk off their financial books."

A victory for Florida families

Many pediatricians use strong language to describe their anger and frustration with the Florida Department of Health and what it did in 2015 to the 13,074 children.

"This has just been a nightmare, and we're still experiencing the fallout," said Dr. Toni Richards-Rowley, treasurer of the Florida chapter of the American Academy of Pediatrics.

"It's disgusting," said Cosgrove, the pediatrician in Merritt Island. "It's all about money and not looking out for the children."

"Honestly, it makes me want to puke," said Lida Sarnecky, nurse manager of the team at the University of Florida that takes care of children with cleft lip and palate.

"In my heart, what I want to do is go down to Governor Scott's office and ask him, 'What if this were your child or grandchild who couldn't receive the care they needed? How would you feel then?' " she said.

By June 2015, some Florida parents had had enough.

Five children, including Alejandro Rodriguez, and Yasmeen and Aref Shabaneh, sued the state Department of Health to get it to stop using the telephone questionnaire to take patients off CMS, claiming that the state Department of Health hadn't gone through formal rulemaking procedures.

The children won.

The Miami Herald declared "Judge slaps Florida for purging sick kids from treatment program."

The state didn't fight the ruling. Instead, it came up with a new way to screen children for the program -- one that doesn't rely on a telephone survey and takes into consideration a child's diagnosis.

Many parents and pediatricians assumed the state would soon reach out directly to parents to let them know they could reapply to have their children put back on CMS.

They were very wrong.

Five months after the judge's decision, St. Petery, the Tallahassee pediatric cardiologist, implored the secretary of the Department of Health to reach out to parents.

To St. Petery, the reasoning was obvious: A judge had said that the state had violated the law. Reaching out to the parents was a way of correcting wrongdoing.

The state had a notice on its website about the ability to be rescreened for CMS, and at a meeting with state legislators, a department official had given out a phone number parents could call. But St. Petery knew that busy parents of very sick children might not attend official state meetings or notice pages on government websites.

"I would hope that you would consider notifying each of the parents of those 13,074 children that the tool by which their child was screened out of CMS has been declared invalid, and that they have the right to appeal that decision," St. Petery wrote to Dr. John Armstrong, then secretary of the Department of Health and the state surgeon general.

Armstrong wrote back that doing so would violate federal regulations, since the children had been switched to other Medicaid insurance plans.

"Federal regulations prohibit direct marketing to children currently being served by another managed care plan," he wrote back to St. Petery.

CNN was unable to reach Armstrong for comment. Gambineri, the Florida Department of Health spokeswoman, said he "is no longer employed by DOH."

Not satisfied with Armstrong's response, St. Petery sought help from US Rep. Kathy Castor, a Democrat from Tampa. Castor took his concerns to the federal Centers for Medicare and Medicaid Services.

On March 23, 2016, an official at that agency sent an email to Justin Senior, then the Medicaid director at Florida's Agency for Health Care Administration. CNN obtained the email under the Freedom of Information Act.

In that email, the federal official explained to Senior that federal regulations do not prohibit Florida from reaching out directly to families.

"To clarify, 42 CFR 438.104 does not prohibit marketing," wrote Jackie Glaze, associate regional administrator for the Division of Medicaid and Children's Health at the Centers for Medicare and Medicaid Services, citing a federal regulation.

More than a year later, on July 24, 2017, the Florida Department of Health sent a letter to parents letting them know that their children could be screened to get back on CMS. The letter was sent to 6,081 parents whose children were removed from CMS and put on another Medicaid plan and were still on that plan and financially eligible for Medicaid, according to Gambineri, the Florida health department spokeswoman.

That letter was sent nearly two years after the judge's decision. Pediatricians say they're angry it took that long to directly let parents know about the possibility of getting back on CMS.

Gambineri said there was concern that parents might get confused.

"It was originally thought to be, and still is considered a risk, in terms of confusion and disruption to families, to send a letter because they have had rescreening available since 2015," Gambineri said a few months before the letter was sent out.

Nelson Mandela and Mr. Rogers

Now that LJ Stroud is back on CMS, he's a happy, strapping 13-year-old who loves to play football and horse around with his brother and sisters in the family's backyard in St. Augustine.

But his mother looks back on the dark days in 2015, after her son was switched off CMS, when she says he would lie on the couch in pain, unable to get the surgeries he needed.

It's not just her son's physical pain that makes Stroud angry; it's his emotional pain.

When LJ was on CMS, Stroud says, he received excellent care and was a contented, well-adjusted child, never thinking of himself as different despite his birth defect.

But she says that when he was in pain because he couldn't have surgery, he started to feel sorry for himself.

" 'Why did God make me this way?' " she says he asked. " 'Why can't I be like my brothers and sisters?' "

When she hears about how top Florida officials have spoken with pride of what they did to her son and to more than 13,000 other children, she becomes livid.

Last year, Armstrong, then Florida's surgeon general and secretary of health, made a presentation to the Florida Children and Youth Cabinet, a panel created by the state Legislature to promote children's welfare.

Declaring that the Department of Health "cares about every child in Florida," Armstrong explained how the state removed the 13,074 children from CMS.

Armstrong's presentation quoted two great advocates for children, Nelson Mandela and Fred Rogers.

First, he quoted Mandela: "There can be no keener revelation of a society's soul than the way in which it treats its children."

And he quoted Fred Rogers, the star of the children's television show "Mister Rogers' Neighborhood": "Anyone who does anything to help a child in life is a hero to me."

Stroud struggles for words to describe what she thinks of Armstrong quoting these two champions for child welfare.

"It's just -- it's just disgusting," she said. "I feel my blood boiling just thinking about it."

Editor's note: The original version of this story has been updated to include a new response from the Florida Department of Health, to clarify the CMS eligibility screening process the department uses currently, and to include the full name and position of one its employees.