ABC News

Christie Brinkley's openness with the press about her ongoing child custody battles with ex-husband Peter Cook is harming their children, Cook told ABC News in an exclusive interview Tuesday in which he also accused her of publicly castrating him and of throwing her family "under the bus" to drum up publicity for her return to Broadway.

"She can use her celebrity to get the media to say 'He's a bad guy.' You know … I'm not trying to sell tickets to anything. I don't want this press. I'm not interested in it. And there's got to be a better way for her to do it. Go do a charitable act or something, get your name in the paper. But stop throwing your family under the bus," the 53-year-old Hamptons architect told ABC News' Elizabeth Vargas.

Cook says he believed Brinkley made their latest court skirmish public to "to coincide with her return to the stage in 'Chicago'," and during the interview he expressed anger and frustration.

"I don't know how you can ever rationalize your way out of fighting to have this private family matter become so public. And children will live with it forever," he said. "I mean, it used to be 40 years ago, it was in the newspaper and it ended up under a bird somewhere. But now it's Google eternity. This will never go away for my children."

In response to the comments Cook made during the interview,  Brinkley's attorney, Tom Campagna, released the following statement:

"Peter Cook has repeatedly broken the confidentiality agreement that Christie has continued to uphold. Peter is the only one to go on national television spewing sexist, disgraceful, demonstrably false lies, which gives a taste of what Christie has had to endure since Peter betrayed his marriage vows. Peter embarrassed himself and hurt his family by having an affair with a teenage girl and admitting to an extensive pornography habit."

The statement continued: "While Christie, a single mother who has been the sole provider for her family, was working on Broadway, he refused Christie access to her children on her one day off. Four months ago, Christie quietly asked the court for Peter to fulfill his child support obligations, and most importantly, to uphold the anti-harassment order preventing his pattern of intimidation and smear campaigns. Sadly, he has chosen to make this his own self-serving publicity tour without regards for his children."

Brinkley, 58, filed court papers last November saying that Cook violated their 2008 divorce court ruling by sending her "aggressive" emails, and accusing Cook of being a deadbeat dad.  Brinkley is seeking $140,000 in fines and an additional $32,000 in educational costs for their children.

In February, Cook filed court papers of his own, alleging that Brinkley owes him money. In those filings Cook reportedly calls his ex a "narcissistic egomaniac" and says he was the primary caregiver for the children while she relocated to New York City to perform in "Chicago" on Broadway.

It was that Broadway turn that may have opened the gates to this newest episode between the exes. Cook said he had paid his child support payments in advance, and had contacted Brinkley's lawyers to see about getting the payment reversed since he says he was going to have the children all the time during the period that Brinkley would be away on Broadway.

Cook, who called the allegations in Brinkley's court documents "hollow and baseless," took exception to being characterized as a deadbeat dad. He said he pays almost twice the child support that is required, and cares for his children, Sailor, 13, and Jack, 16, full time, affecting his ability to earn a living.

Cook claims his ex-wife has scheduled activities for the children during time when they're supposed to be with him, and that she often fails to inform him of when they have important activities.

"I plead with her lawyers to please tell your client to schedule on her own time. She's required to tell me about doctors' appointments. She's required to tell me about dentist appointments. She's required to keep me on equal footing. And she does none of it. I get nothing. I get no respect as a father until it's time to ask for a check," he said.

"The real victim in this is not me," he added. "It's the kids, who have to have this re-hashed and brought back in the public eye over and over and over again. It's unnecessary. I'm a good father. I love my kids. I accept my responsibilities with my children. I accept my legal responsibilities to her. I follow the rules and all I ask is that she do the same thing," he added.

Campagna, Brinkley's lawyer, told ABC News that she has sole custody of the children, and anything suggesting otherwise was "delusional."

Brinkley is reportedly worth tens of millions of dollars. When Vargas asked Cook why Christie would bill him and squabble in court over expenses that are just a few hundred dollars, he said he believed it was a way for her to harass him.

"Moneyed people and celebrities can abuse the legal system. … For her to spend $100,000 on lawyers just to jerk me around, it's no - it's no sweat for her," he said. "For me, it's a significant cut in my net worth and my future and my kids' futures with me."

If he were indeed a bad guy, Cook asked, why would Brinkley leave the children with him while she went off to do Broadway?

"Which is it? Am (I) the villain that you're going to publicly castrate, as she's doing currently in the press? Or am I the good dad? Because in a few weeks, she's going to surrender the kids to me again, full time. But it can't be both," he said. "And that's unfair to the kids, to be doing this to their father."

Over the weekend, members of Brinkley's camp told the Daily News that Cook keeps harassing her and smearing her reputation, while Cook's attorney countered that Brinkley was a "second-rate celebrity starved for attention."

Brinkley, a former Sports Illustrated swimsuit cover model, filed for divorce after Cook confessed to an affair with 18-year-old staffer Diana Bianchi and to viewing pornography online during the marriage.

He admitted to paying Bianchi $300,000 to keep the affair quiet.  Speaking about his indiscretions during the marriage to ABC News' Barbara Walters in a 2008 interview, Cook  said the affair started because his "needs hadn't been taken care of."

"I wanted a little acknowledgement, a little attention, a little thank you every now and then, for my efforts," he told Walters.

Cook told Vargas he regrets settling in the divorce because he never got his side of the story out. He's determined to see this through to trial.

"I settled to try to make peace and try to make things easier on my kids and it's thrown back in my face again," he said. "And so this time I'm not going to allow it to happen. I'm going to let the judge, going to let everybody see what's been going on and make their own decisions."