During their 12-year marriage Cook had one daughter with Brinkley, named Sailor, and he also legally adopted her son with ex-husband Richard Taubman, Jack Paris.
The pair has been locked in a war of words over its divorce settlement since the two split in 2008 and this week (begs27Feb12) Cook filed legal papers against his former wife at New York's Suffolk County Supreme Court, alleging he shouldn't have to pay the beauty upwards of $32,000 (£20,000) in back child support payments.
According to the New York Post, the businessman claims he's owed $25,000 (£15,625) because he looked after their two kids for five months while Brinkley performed in the musical Chicago on Broadway and in London's West End.
Neither star has publicly addressed the new legal battle, with Cook telling the publication, "I can't comment on any of that."
The veteran supermodel has wed four times - to French artist Jean-Francois Allaux, rocker Billy Joel, businessman Richard Taubman and Peter Cook.
She is mother to three children, all from different relationships, and although she's open to love again in the future, she's adamant she'll never exchange vows with another man after the drama of her divorces.
Brinkley tells Britain's Stella magazine, "I can now say unequivocally that I would never get married again. There's absolutely no reason to.
"I learned in my divorce that marriage is ridiculous. You take a vow but you don't get brownie points when you honour your vow and the other person doesn't.
"The court doesn't recognise that. It's like, 'All right now, let's see how we're going to divvy up the kids.' Well, obviously, the one that didn't break the vows should be the role model, but no."
Brinkley's last marriage, to Cook, came to an end in 2008.