Sunny, Chandler and Jesse Jr. -- James's children from previous relationships -- are living with Bullock at an undisclosed location, an insider close to the couple told the entertainment news Web site.
"It's a positive sign about Sandra's relationship with Jesse," the source said without offering any details.
The news comes weeks after a tattoo model and stripper announced she had a long-term affair with James while he was married. Several other women have since come forward to claim they, too, had sex with James during his five-year marriage to the best-actress Oscar winner.
Bullock reportedly has moved out of the home she shared with James, who has been undergoing treatment for unspecified personal issues.
The actress has not personally made any statements regarding the many salacious stories surrounding her marriage, other than to contradict an online report this week that said she made a sex tape with James.