JOHNSON COUNTY, Ind. — The children fell ill, one by one, with cancers that few families in this suburban Indianapolis community had ever heard of. An avid swimmer struck down by glioblastoma, which grew a tumor in her brain. Four children with Ewing’s sarcoma, a rare bone cancer. Fifteen children with acute lymphocytic leukemia, including three cases diagnosed in the past year.

At first, families put the illnesses down to misfortune. But as cases mounted, parents started to ask: Could it be something in the air or water?

Their questions led them to an old industrial site in Franklin, the Johnson County seat, that the federal government had ordered cleaned up decades ago. Recent tests have identified a carcinogenic plume spreading underground, releasing vapors into homes.

Now, families in a county that voted overwhelmingly for President Trump are making demands of his administration that collide directly with one of his main agendas: the rolling back of health and environmental regulations.

On Wednesday, a group representing dozens of concerned parents called for a federal investigation by the Environmental Protection Agency’s Office of Inspector General — the same watchdog that examined the government’s slow response to the water crisis in Flint, Mich. — into why Franklin’s toxic plume of trichloroethylene, or TCE, persists.

The group accuses the E.P.A. of "serious mismanagement" and "significant delays" at the site, even after the dangers became apparent this summer, according to a letter the group said it sent to the E.P.A.’s Office of the Inspector General.

But the parents’ demands also reach well beyond immediate concerns about the chemicals under their feet.

Families across the political spectrum have also spoken out against the Trump administration’s drive to weaken restrictions on TCE, a colorless fluid with a subtle, sweet odor used by as many as four-fifths of the nation’s 65,000 dry cleaners, as well as about 2,200 factories and other facilities. Decades ago, it was used at the Franklin site.

Twice last year, parents from Johnson County traveled to Washington to urge the administration to stick with stronger controls.

"We are done begging," said Kari Rhinehart, the mother of Emma Grace Findley, the 13-year-old swimmer who developed brain cancer and died in 2014. "We are demanding the E.P.A. finish what it started and place these restrictions on TCE and other dangerous toxins."

The E.P.A. confirmed that the chemicals were present near the Franklin site and said that fewer than 10 of 37 homes it had tested had potential air quality issues. The agency said its testing was continuing and that, if necessary, homes would be fitted with devices to clean the air.

Declaring TCE "carcinogenic to humans by all routes of exposure," the Obama administration had sought to restrict two of its riskiest uses, as a stain remover and as a degreaser, and had marked it for further review, potentially to ban the chemical altogether. It had also moved to strengthen cleanup rules for hundreds of sites nationwide believed to be contaminated.

But at the urging of industry groups, the Trump administration has stalled some of those moves. In 2017 it indefinitely postponed the proposed bans on risky uses, leaving as many as 178,000 workers potentially exposed. It also scaled back a broad review of TCE and other chemicals so that it would exclude from its calculations possible exposure from groundwater and other forms of contamination — the problems present in Franklin.

In Johnson County, a parents’ group co-founded by Mrs. Rhinehart, If It Was Your Child, has traced at least 58 childhood cancer cases since 2008. At 21.7 cases of pediatric cancer per 100,000 children, Johnson County’s rate puts it in the 80th percentile among counties nationwide, according to data for 2011-2015 from the National Cancer Institute. Both the national and Indiana average are fewer than 18 pediatric cancers per 100,000 children.

"You don’t expect to see so many cancers in a relatively small community", said Dr. Paolo Boffetta, professor in environmental medicine and public health at the Icahn School of Medicine at Mount Sinai in New York. Even so, he stressed that there was little research linking childhood cancers to TCE. "This doesn’t mean an association doesn’t exist," he said. "But studies have not been able to confirm it."

Motria Caudill, a scientist at the federal Agency for Toxic Substances and Disease Registry, which investigates environmental hazards, said at a community meeting in Franklin in November that it was still too early to draw conclusions. Her agency was still working with others, she said, "just to see what is going on."

The TCE contamination has been traced to a former factory that, for years, discharged industrial wastewater into a municipal sewer. Amphenol, an electronics maker based in Wallingford, Conn., became responsible for the cleanup after acquiring the site, though it no longer owns the property.

In June, tests by an environmental group, Edison Wetlands Association, working with parents, detected the chemical in the air at two homes and in outdoor air near the site. The findings prompted more tests by local and state government officials, including one by Franklin that found levels more than 250 times state limits around a sewer near the homes. In November, the E.P.A. identified a plume of contamination stretching beyond the site toward nearby homes.

Joseph Bianchi, an Amphenol spokesman, said the company was working "to help ensure the well-being of residents," and the E.P.A. has promised to team up with the company on a cleanup plan. But at the November community meeting, patience wore thin.

"When will this cleanup be done and gone," asked Sonya Hallett, a local philanthropy consultant and mother of one, "and not hazardous to people who are living around it?"

Trouble Beneath the Grass

The state investigators who descended on Jennifer Clark’s house in October drilled into her basement floor. They sought signs that chemicals in the ground were turning into a vapor and rising into her home, a phenomenon known as "vapor intrusion."

Her daughter Chelsea learned when she was 12 that she had acute lymphoblastic leukemia, a cancer of the blood and bone marrow. After chemotherapy, Chelsea, now 18, is in remission; she dreams of working in the beauty industry.

But over the summer, the Clarks received daunting news. Tests at their home on behalf of the Franklin parents’ group detected TCE levels more than 18 times federal limits.

Testing is tricky. Results can be affected by the weather or even by doors left open, said Kelly Pennell, associate director of the federally funded Superfund Research Center at the University of Kentucky. Indeed, later tests showed lower levels in the house.

Still, the Clarks remain worried. Their youngest daughter is now 12. "This is our forever home right here, where the kids are going to come back with the grandkids," Mrs. Clark said.

They live about a mile and a half from the former industrial site in Franklin, now a patch of grass bordered by old railroad tracks to the north and neat rows of homes to the south.

Amphenol agreed to a cleanup in 1990, installing a "pump and treat" system that was supposed to control the contamination. For decades Amphenol pumped out groundwater, but contamination remained.

The technology’s apparent ineffectiveness raises questions about hundreds of other sites using it, said Shannon Lisa, program director at Edison Wetlands.

"How many other communities across the United States are facing these very same issues?" she said.

One Home, Two Families, Two Cancers

Two girls lived, several years apart, in the same Franklin apartment about a mile from the toxic site. Both developed cancer, one at age 8 and the other at 14.

"You can’t go anywhere, or do anything, without meeting someone who’s been affected," said Angela Brennan, whose daughter, Karley, was one of those girls. In 2012, the family learned that Karley had cutaneous T-cell lymphoma, a rare cancer affecting the skin. Later that year, 14-year-old Madison Newton was told that she had an aggressive form of pilocytic astrocytoma, which causes tumors in the brain and spinal cord.

Karley, who turns 15 this week, is in remission. Madison died in 2015. And across Franklin, If It Was Your Child yard signs dot the city, where a local TV station, WTHR Channel 13, is doggedly tracking the concerns.

There are conflicting views in Johnson County of the administration’s environmental rollbacks. There is talk that the federal government should get out of people’s lives, even as local officials have called on the E.P.A. to take over the response to the contamination.

"When it comes to public health, we can go against party lines. And I don’t agree with trying to roll back the E.P.A.’s role," said Steve Barnett, Franklin’s mayor and a Republican. "Back in the day, there weren’t any rules. That’s why there was so much contamination," he said.

Many members of If It Was Your Child in the Franklin area play down the politics, noting that both parties have let the cleanup fall by the wayside. Nevertheless, their demands come at a time when the Trump administration has weakened the very rules that could prevent another Franklin.

"We should not have to fight Republicans or Democrats to save our children. It’s not a political fight for us," said Stacie Davidson, a Trump voter who co-founded the parents’ group with Mrs. Rhinehart (who didn’t vote for Mr. Trump).

Mrs. Davidson said, "His loosening of E.P.A. regulations, it’s infuriating." She added, "We’re ruining the environment for money."

Mrs. Davidson learned in 2014 that her stepson, Zane, who was 10 at the time, had a rare form of leukemia. He is now in remission. She has traveled to Washington to speak in favor of stronger TCE regulations. "What we’re fighting for is seemingly being undone right now," she said.

Still, she said, she did not regret her vote. "Trump’s a businessman. There are great things he can do for our country. But he’s used to building high rises for money," she said. "He’s not as environmentally savvy. Our hope is that he surrounds himself with people who are more knowledgeable."

Despite the emergence of alternatives to TCE, the Trump administration has stalled action on restricting its use. "There have been greener alternatives to TCE for years," said Tom Forsythe, an executive vice president at Kyzen, a Tennessee cleaning-materials company, who joined E.P.A. officials in a conference call in August 2017 to lay out other options.

But a few months later, in October, when E.P.A. officials visited the Integer medical devices factory in Minneapolis, Minn., the agency received a different message.

"According to Integer, there are no effective alternatives," read an E.P.A. memo about the visit, which was arranged by a chemicals group, the Halogenated Solvents Industry Alliance. Dry cleaners have also lobbied against a tightening of protections, arguing among other things that substitutes could harm clothing.

"Yes, we have spoken to E.P.A. about our desire not to have TCE banned — as is our right of free speech," said Faye Graul, the chemical group’s executive director. TCE "is used in tightly controlled industrial settings," she said, "with controls in place so that no workers are harmed."

Looking to the Future

Johnson County bills itself as the festival county. In December, it hosted a holiday parade and a drive-through Nativity with live actors. And the economy is strong. A technology park measuring nearly a million square feet is soon opening in Franklin.

"I see good things that Trump has done," said Mr. Barnett, the mayor, emphasizing his town’s future. "The economy’s good. There’s been a lot of investment into our city."

Recently, though, Mrs. Rhinehart has been thinking of the past. Four Christmases ago, her daughter Emma Grace suffered two severe seizures.

"She said, 'Mommy, something’s not right,' and I knew we weren’t going to get much more time," Mrs. Rhinehart said, recalling their final conversation. "I gave her some medication and she drifted off to sleep."