"His parenting has to be away from his home and he can't expose them to the `20/20' broadcast" airing Friday night, Cohen said.
The attorney also filed papers in Suffolk County seeking a temporary restraining order; the divorce became official Sept. 29.
Cook's attorney, Norman Sheresky, did not immediately return a telephone call seeking comment.
Cook, an East Hampton architect, settled the highly public and nasty divorce last summer following a weeklong trial that featured salacious testimony about his affair with a teenager and his use of Internet porn.
He explains those allegations in the interview.
"I was seeking a connection I could not find in my own marriage," he told Walters. "I think the emotional aspect of our lives had changed. I think we were both feeling more like we were living with a brother and sister than a life partner."
Cook said he agreed to the interview hoping, "the world will see that I'm not the scumbag pervert that I've been painted to be. The misinformation that came out during the trial is the elephant in the room. It's the elephant in the room for my kids."
The divorce settlement gave Brinkley custody of the couple's 10-year-old daughter Sailor and 13-year-old son Jack, whom Cook adopted. Jack's biological father was Brinkley's third husband. Cook got $2.1 million from the supermodel, as well as liberal visitation rights.
The marriage was Brinkley's fourth and Cook's first.
