Hillary Rodham Clinton kindled sharp partisan debate last year when critics accused her of supporting the right of children to sue their parents. And the riveting Gregory Kingsley case in Florida stirred fears that children would go to court to divorce their parents. Children's advocates applauded Clinton's views and the Florida ruling, arguing that children often need independent representation and a greater voice in legal proceedings affecting their interests. But conservatives warned that greater legal rights for children threatened parental authority and traditional family values. Now, with Bill Clinton in the White House and Hillary Clinton at his side, conservatives worry that government involvement in family issues will expand. They are pressing for a return to traditional values as the best remedy for the ills besetting America's children.