Brinkley was ordered by a judge to return to court today just hours after the former supermodel's lawyer Peter Coronia released a statement claiming a settlement that exonerated her.
One of Cook's lawyers, Steven Kuhn, told ABCNews.com that Coronia had "jumped the gun by releasing a press release" before an agreement that had been hammered out overnight before it was presented to the judge.
Judge Mark Cohen refused to approve the agreement until Brinkley showed up in court. When Cook and his attorney appeared this morning alone, Cohen ordered Brinkley to appear as well, telling her attorney that he didn't care where she was, but that she needed to get in a car and start driving.
Both sides claimed victory.
Earlier in his statement, Coronia said Brinkley was "vindicated" because the settlement did not include any of Cook's requests that Brinkley "undergo anger management" or that a "parenting coordinator" be appointed for the couple's two children, Jack and Sailor.
Kuhn also claimed that Cook got what he wanted.
"We reached a final and full settlement," Kuhn said. "Mr. Cook accomplished a lot in these proceedings, but it should never had been necessary had a simple court order been followed. Mr. Cook is unhappy that he had to come to court to enforce his parenting rights."
Kuhn said Cook received "makeup time" he lost with his son when Jack couldn't travel on a class trip to Egypt last Thanksgiving because he didn't have his passport. He also received better provisions for the exchange of the children's passports.
Cook filed a complaint against Brinkley after she failed to deliver Jack's passport to Cook last year. Brinkley had claimed she arranged for one of her employees to drop it off when she had to race to be with a friend who had just lost her mother.
Brinkley filed a counter claim, accusing Cook of violating terms of their divorce agreement, finalized a year ago. Both demanded that the other be jailed for the violations.
The rancor continued today outside the courtroom when Brinkley called Cook an "extreme narcissist" in front of reporters.
"Google 'Divorcing a narcissist,' " Brinkley told reporters. "It will give you a lot of insight into what I've been going through for the past three and a half years."
Cook shot back: "I'll accept 'narcissist' over 'interference.'"
In their release early this morning, Brinkley's lawyer charged, "Since Mr. Cook lost the custody battle in the divorce trial, he has staged a relentless smear campaign against Ms. Brinkley. Mr. Cook has tried repeatedly to tarnish Ms. Brinkley's reputation by making defamatory statements during national television broadcasts, in print media and blogs."
Coronia claimed Cook's alleged attacks violated the couple's confidentiality agreement.
"For the sake of the children, she is hopeful that Mr. Cook will cease his attacks on the children's mother," the statement concluded.
Also as part of Tuesday's settlement, Cook will get more time in the summer with his children. Kuhn said the former golden couple will alternate weeks with the children, dividing pre- and post-camp time equally.