It is late afteroon and 11-year-old Daniel Carter is sitting in his specially designed wheelchair in the playroom of the Hospital for Sick Children awaiting the arrival of his visitors.

When his mother, Nellie Carter, walks into the room, a smile that only a mother and son can share plays across their faces.

She walks over to him with her arms outstretched and nuzzles him gently. She begins singing "My Pretty Baby," one of his favorites, and the smiles grow even wider.

But visits like this between Daniel and his mother are rare.

Daniel is profoundly retarded, unable to walk, speak or do any of the other things that most 11-year-old boys enjoy. For the past seven years, Daniel has been a patient at the hospital, separated from his mother, brother and two sisters who live in a crumbling three-bedroom apartment in the 456-unit Greenleaf Gardens public housing project in Southwest.

Although Nellie Carter, 31, said she desperately wants Daniel at home, she wants him to remain at the hospital until the D.C. Department of Housing and Community Development grants her request for a transfer to a larger and cleaner apartment.

"We don't have heat or hot water," Carter said of the apartment where she has lived since 1981.

"I had to go out and find two cats to fight the rats, and the incinerator across the hall stays stopped up. I don't want to be in here, and I don't want my babies in here. Danny's not coming home until they find a better place for us," she added.

Greenleaf Gardens, a combination of two-story barracks-like buildings and two multistory buildings near the intersection of M Street and Delaware Avenue SW, has been labeled by city housing officials as one of the District's 10 worst properties.

A nine-story building at 1200 Delaware Ave. SW, containing 214 units, once the centerpiece of the project, was closed by city officials last year after it was overrun with drug dealings and crime and became a chronic victim of vandalism.

Hospital officials said Daniel needs a room of his own that can accommodate a hospital bed and other essential special equipment.

Carter said she has been requesting a transfer to a four-bedroom apartment for two years, but she said resident managers at the housing complex told her there was a "freeze" on transfers and that no larger apartments were available. The Hospital for Sick Children supports Carter's decision, and Alvita Roberts, Daniel's caseworker at the hospital, has been acting as a liaison between Carter and housing officials.

"She wants to keep her family together, and we support her in that feeling," Roberts said. "She cares about her children, but she also wants a safe and proper environment for them. Right now, it's in Danny's best interest to keep him at the hospital."

Charles Draper, the city's new public housing administrator, denied that there was a freeze on apartment transfers, and he said he was unaware of Carter's request until he received a letter from the National Housing Law Project, a nonprofit group that specializes in helping tenants who live in publicly funded housing. Carter went to the group for help several months ago.

Draper added that Carter's request is complicated because Carter, with three children -- Frederick, 9, Ethel, 7, and Pamela, 3 -- has allowed three unspecified people to live in the three-bedroom apartment. Draper added that Carter is several months behind in her rent.

"Our records indicate that several people that were not on the original lease are living in the apartment," Draper said. "So it's not necessarily an issue of finding a larger apartment; what's important is whether or not these other people are planning to move out. There are some things that will have to be straightened out before we can consider a transfer," Draper said.

Carter denies that any unauthorized people are living with her. "The only other person I have living here is my niece, and she is on the lease," Carter said.

Carter said she had been withholding rent for five months hoping to force officials to make needed repairs. But she said she has given up the rent strike and has repaid all but two months' worth. She is making the repairs herself, she said.

The National Housing Law Project, in its letter on Carter's behalf, suggested that the city was violating federal housing statues that require it to provide a unit to fit Daniel's special housing needs.

The law project has since referred Carter's case to the Washington-based law firm of Wald, Harkrader and Ross, which has agreed to represent Carter free of charge.

Carter's visits with Daniel at the hospital are limited to about one a month because she must get a ride from her brother or a friend. She would have to take three buses to get from Southwest to the hospital on the other side of the city at 1731 Bunker Hill Rd. NE, and she must leave her other small children at home because she cannot afford the bus fare for them, she said. She cannot afford the round-trip cab fare of $10, she said.

"I try to see him as often as I can, but he must think his mother has abandoned him," Carter said. "But I just want a decent place for him to live," she said.

Despite her hectic schedule of raising her three other children, Carter said the special attention and round-the-clock care that Daniel requires would not make him a burden.Most of all, Carter said, after seven years she is anxious to have her oldest son home for Christmas.

"We'd have a nice Christmas because all the family would be here. It hurts not to have him here, especially on the holidays."