Under President Reagan's order, federal authorities yesterday arranged for a desperately ill Gaithersburg toddler to continue to be cared for at home, rather than return to hospital care costing three times as much.

The President interceded after Fredrico and Geraldine Broom, whose son, Don, 2 1/2, has congenital heart and lung problems, sent a Mailgram to the White House asking that their insurance carrier's 90-day limit on coverage of home health care be lifted.

Coverage for the child, who has spent most of his life in Children's Hospital here, would have expired at midnight Monday. "I told Mr. Reagan I needed his help," said Fredrico Broom, a power plant worker at a National Institutes of Health building in Bethesda. "It's essential to his life that he stay at home, where we can give him the time and attention he needs."

His son, who was born prematurely, is blind, deaf and has reduced heart and lung capacity. He requires daily oxygen, a respiratory monitor and nine medications.

Broom said the cost of medical supplies and round-the-clock nursing provided at home is about $4,500 a month, about one-third the cost of hospitalization.

Don Devine, director of the Office of Personnel Management, which negotiates health insurance contracts for all federal workers, yesterday ordered Blue Cross-Blue Shield to continue paying for the child's health care at home for an indefinite period.

"We do this rarely; only when it's cost-efficient," said Pat Korten, spokesman for OPM, who said the agency had been directed by White House officials to request the waiver.

"It is crazy to require the child to receive more expensive treatment at a hospital," Korten said.

Korten said the waiver would last at least until the annual contract with Blue Cross-Blue Shield expires at the end of December. "We do have the authority to direct waivers of contract," said Korten, who noted that Blue Cross-Blue Shield, which insures 40 percent of federal workers, did not object to the request.

The Brooms' case is not the only time the White House has been involved in keeping a child out of hospital care at the parents' request. In November 1981, President Reagan made a national example of an Iowa girl whose parents could not treat their child at home because federal Medicaid regulations only allowed payment for her care in hospitals, not at home.

Broom said he decided to contact the president after learning that the formal waiver process could take up to six months. Broom said the organizer of a Baltimore group, Sick Kids-Involved Parents (SKIP), supplied him with a White House contact and a telephone number.