Brinkley has been locked in a bitter child support battle with her former partner ever since they split in 2008 following allegations Cook had an affair with a teenage store clerk.
Their court fight has turned ugly in recent months, with both parties accusing the other of leading a public smear campaign - but at a Long Island courthouse on Friday, the former couple was urged to resolve the issue for the sake of its kids, Jack, 17, and Sailor, 13.
However, the pair failed to reach an agreement after hours of negotiations and according to the New York Post, the architect's new wife Shaw, who he married on Valentine's Day (14Feb12), was dragged into the war of words - with the model saying, "When you find out he's been cheating on you, I'll be here for you."
Shaw reportedly took the comment in her stride and later told the publication, "What she's done to these children over the past six years - there really aren't words. To embarrass and humiliate the father of your children only humiliates and hurts your children."
Brinkley and Cook are expected to return to court on Tuesday (26Jun12).