Peter Cook insists his former wife should stop being so open about their court affairs, and accuses Brinkley of throwing her family "under the bus" to promote her return to Broadway in the musical Chicago.
He tells ABC News, "She can use her celebrity to get the media to say, 'He's a bad guy....' 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.
"I don't know how you can ever rationalise your way out of fighting to have this private family matter become so public. And children will live with it forever. I mean, it used to be 40 years ago, it was in the newspaper and it ended up under a bird somewhere. But now it's Google eternity. This will never go away for my children."
Firing back at Cook's comments, which he made while filming a news segment for America's Nightline show, Brinkley's attorney, Tom Campagna, says, "Peter Cook has repeatedly broken the confidentiality agreement that Christie has continued to uphold. Peter is the only one to go on national television spewing sexist, disgraceful, demonstrably false lies, which gives a taste of what Christie has had to endure since Peter betrayed his marriage vows. Peter embarrassed himself and hurt his family by having an affair with a teenage girl and admitting to an extensive pornography habit.
"While Christie, a single mother who has been the sole provider for her family, was working on Broadway, he refused Christie access to her children on her one day off. Four months ago, Christie quietly asked the court for Peter to fulfil his child support obligations, and most importantly, to uphold the anti-harassment order preventing his pattern of intimidation and smear campaigns. Sadly, he has chosen to make this his own self-serving publicity tour without regards for his children."
Brinkley filed court papers in November (11), claiming Cook had violated their 2008 divorce court ruling by sending her "aggressive" emails.
The funnyman woke up in a panic when he heard an explosion from underneath his bus during a trek across North Dakota.
The driver and passengers escaped unscathed, but Cook admits he was so shaken when the vehicle stopped he evacuated wearing only a sock and his underwear.
Appearing on U.S. programme The Tonight Show with Jay Leno, he explained, "(It was) 3:30 in the morning, we're all asleep - tyre explodes.
"When a tyre explodes you don't wake up and go, 'A tyre just exploded!' You think a bomb has gone off... so a couple of things happen. First thing, you sit up and the driver's trying to compensate and he's swerving on the highway and you're flying back and forth on the bed... The bus then fills with smoke."
Showing a picture of himself posing shirtless with three pals outside the bus, he laughed, "We were freaking out."