SINCE COMING TO THE UNITED States this fall to study, Prince Thumbumuzi Dlamini, Zenani Mandela's husband, has taken on two tough public relations battles for the family.

His first fight involves the Home Box Office movie "Mandela," which portrays the love story of Nelson and Winnie Mandela. Dlamini says no one in the family was contacted about the making of the movie and no profits are being shared with the family. John Kelley, publicity director for Home Box Office, says "attempts were made to contact Winnie Mandela early on." The film, starring Danny Glover and Alfre Woodard, has been condemned by Winnie Mandela as serving "no political purpose . . . The producers are just cashing in on the name of the family." Kelley says Home Box Office "did not make any money from the film."

Dlamini's second fight is over news reports that Nelson and Winnie Mandela are feuding over her decision to build a five-bedroom, $350,000 house on a hilltop overlooking Soweto. Although the house is quite large, Dlamini says, Winnie Mandela cares for 25 Soweto orphans and some will live with her in the new house.

"I have been involved from the beginning, when I took plans for the house to Daddy in jail," says Dlamini. "Some people have said Mummy is using ANC funds to build the house. She is using no one's funds. Some of the money is derived from royalties on the book Part of My Soul Went With Him. She has never used the movement's funds. All this talk about jacuzzis, pools, is totally untrue."