Christie Brinkley, Peter Cook

AP Photo/Mary Altaffer

Christie Brinkley and Peter Cook's divorce itself was messy, but four years later the mudslinging continues.

The model-actress, 58, and her architect ex-hubby are back in court, both claiming the other violated the terms of their divorce agreement.

While Cook tells ABC News he thinks his ex wanted their court battle to be public "to coincide with her return to the stage in Chicago," Brinkley's attorney tells E! News that Cook's claims are "delusional"...

Lawyer Tom Campagna said in a statement that Brinkley "will not take the bait," but that she "will stand up for herself and her children and refuses to be bullied." As well, Campagna also refutes Cook's claims that he paid more than he was asked in child support, adding, "he's been regularly behind in payments."

So what did Cook claim exactly?

"She can use her celebrity to get the media to say, 'He's a bad guy,'" Cook, 53, told ABC. "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."

Cook explains that he didn't pay child support last year because "the children were in my full-time care."

"I'm here, not to attack Christie Brinkley, but to defend myself," he says. "To be called a 'deadbeat dad' to me is such a horrible, spiteful thing to say, besides the fact that it's totally untrue… I pay more child support than I was required to by court.

"I do the kids' laundry, I cook the kids' food. I drive them to school. I run their errands. I do their homework with them. It's me," he says. "With [Brinkley's] resources, if I was a bad guy—if you had $80 million dollars—would you let a bad guy have your kids for a day? Or would you fight him so he never has contact with those children again? 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. So which is it? Make up your mind, but it can't be both."

Brinkley's attorney said that it's per court order that the children are put in Cook's care when she's away for more than two days., "[It's] something Christie fought against," he adds.

"The Court granted Christie sole legal and residential custody and final decision making power for their children," the statement continues. "Peter's claims of being the 'primary caregiver' are delusional."

—Additional reporting by Maureen Heaton

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