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.
Cook Confided in Barbara Walters
A year ago, in his first interview since his bitter public divorce from Brinkley this summer, Cook told Barbara Walters that "I felt like I was a guest in someone else's life" and said he had an affair with a teenager because he was "seeking a connection I could not find in my own marriage."
Many were shocked when Cook and Brinkley split after 10 years of what from the outside looked like a perfect marriage. Their divorce proceedings this summer were some of the ugliest in recent memory.
Cook spoke to Walters about what went wrong, his affair with a teenager and the $300,000 payout to her, his reported $3,000-a-month Internet pornography addiction and why he was willing to have his dirtiest secrets revealed in the fight over access to their children after the divorce.
Cook told Walters why he started an affair with the young woman in 2005, when he had a great marriage in 2004.
"I was seeking a connection I could not find in my own marriage," he said. "I think the emotional aspect of our lives had changed. I think we were both feeling more like we were living with a brother and sister than a life partner. … I think I just suddenly realized when I was getting attention from someone else that this is something that is missing in my life."
When asked what he wanted, Cook said, "I wanted a little acknowledgement, a little attention, a little thank you every now and then for my efforts, for the amount of time I took to care for her and my family, for the wealth I was building. Just the tremendous amount of work I was putting into my family. … My world became her world. It had to be that way. … There came a time when I pulled up [to] the driveway to the home that I found, that I built, that I lived in, and I felt like I was a guest in someone else's life."
Cook said that he agreed to be interviewed to try to "correct some of the wrongs."
"My hope is that the world will see that I'm not the scum bag pervert that I've been painted to be," he said. "The misinformation that came out during the trial is the elephant in the room. It's the elephant in the room for my kids. And I'm hoping maybe if I can correct some of the wrongs."
When asked whether he wanted his ex-wife to see the interview, Cook said, "I don't think I can avoid that. But I think if she does, what I hope comes of it is that she takes the time to heal herself. And she goes back and remembers that I made a mistake, but that I am that person that she wrote the poems about, that she raved about in magazine articles and anybody who she could get … twist their ear to listen. I am that person today, that I was then."