Parents of children at the Cheltenham Center for emotionally disturbed youths in southern Prince George's County have asked Gov. Harry R. Hughes to stop the break-up of the center's six-year-old program this June.

After a series of disputes with the Maryland Department of Health and Mental Hygiene, the Prince George's school board voted unanimously in November to abandon its support for Cheltenham, and to end its educational programs there this summer.

Since then, parents, teachers and 80 children at Cheltenham have learned to live with uncertainty while the center's two principal partners--the state and Prince George's County--make plans to part company. A boiler blowout at the school, which forced closure of the main building for the last three weeks, has added to the center's problems.

Parents and teachers at Cheltenham reacted to the school board's decision by forming a PTA in an effort to preserve the center and the programs they consider successful. Not only have they asked Hughes to intervene by imposing a moratorium that would stop the breakup of the center, but in an effort to bring the disgruntled parties together again they have invited the governor, Health Secretary Charles S. Buck Jr., and state and local school officials to a meeting at Cheltenham next month.

Although he has yet to receive word that Hughes will attend, PTA President Thomas E. Goodrich Sr. said, "We are eventually going to end up in the governor's office." He described the parents' opposition to the breakup of Cheltenham as "vehement."

Meanwhile, the health department and the school board already are finding it difficult to design a program that combines mental health care and education without each other.

After the school board's decision to pull out, the state health department began making plans to seek a private contractor to operate Cheltenham. But it has yet to decide how to provide educational programs without the school board's participation.

The school board, which could not assume responsibility for the 20 residential students at Cheltenham, created a task force to come up with a plan for its own facility for the 60 day students, free from health department interference. But in an effort to arrange mental health care for the students it is responsible for, task force Chairman Robert T. Coombs is now negotiating with the health department.

Last week, school board member Jo Ann T. Bell, who introduced the motion to withdraw from Cheltenham and is a member of the center's board of directors, told the school board it should view its plans to withdraw as a back-up plan only, "in case everything else falls through." Schools Superintendent Edward J. Feeney agreed but said the board should prepare plans to follow through on the decision to withdraw if necessary. "Don't let go of the lever you have going for you," he told the board.

Bell said there is a strong feeling among the directors that Cheltenham should be kept intact, but she is opposed to the idea of the governor issuing a moratorium to stop the breakup. "The problem with that is that right now you have the governor's ear as you never had it before," she told school board members. "It's my belief that if we wait until 1983, the year of the election will be gone" but Cheltenham's problems will remain.

Bell said a more important, immediate goal is to obtain guarantees of state funding. Money is an important consideration for the school board. Its decision to withdraw from Cheltenham came after the health department threatened to withhold funding unless Cheltenham agreed to reserve five of its 20 residential beds for children sent to the center by courts.

The health department offered no money to pay for these children and Cheltenham Director Henry T. Gromada, who argued that the center already was underfunded and inadequately housed, supported the board's action at the time. "There's no way the school system can, or should, meet those demands," he said.

The center takes children from Prince George's, Charles, Calvert and St. Mary's counties. A 1979 plan to build a new center in Prince George's and open a second one in the southern counties was thwarted when funds could not be found.

The center combines psychiatric and educational programs. Small classes and individual attention help the students, who are normal or above normal in intelligence, learn to cope in a school environment and, eventually, return to regular public schools.