Cook, 53, says in a Daily News blog that Brinkley, 58, is "far more concerned with the mirror than our children."
"Her Billy Joel Uptown Girl music video fame faded long ago and the only thing left for her to garner media attention is to continue to publicize the tawdry details of her 'nasty divorce' from her fourth failed marriage," Cook said of his former wife.
The sharp words from Cook, a Hamptons architect, come after Brinkley's legal team and friends spoke out to the Daily News over the weekend to accuse Cook of "intimidation" and orchestrating an "ongoing smear campaign" after he filed a 91-page document at Suffolk County Supreme Court in New York on Feb. 24 alleging that Brinkley owes him money.
In the filings Cook reportedly calls his ex a "narcissistic egomaniac" and says he cared for the couple's kids while she relocated to New York City to perform in "Chicago" on Broadway.
"This is the work of a second-rate celebrity starved for attention," Cook's attorney, James Winkler, said in a statement Sunday. "Brinkley now uses Mr. Cook's response to her motion to generate attention for herself in advance of her return to Broadway regardless of the impact on her children."
The couple separated in 2008 and have been engaged in a bitter custody dispute ever since.
They have one child together, Sailor, 13, and Cook adopted Brinkley's son Jack, 16, by her third husband, Richard Taubman.
Brinkley also has a daughter, Alexa Ray, 26, with her second husband, Billy Joel.
Brinkley filed court papers last November saying that Cook violated their 2008 divorce court ruling by sending her "aggressive" emails and accusing Cook of being a deadbeat dad. She's seeking $140,000 in fines and additional $32,000 in educational costs for their children.
In his filings, Cook is demanding more than $200,000 in fines against Brinkley for the same harassing behavior, according to Winkler.
Brinkley, a former Sports Illustrated swimsuit cover model, filed for divorce from Cook in 2008 after he confessed to an affair with 18-year-old staffer Diana Bianchi and to viewing pornography online while they were married.
He spoke out about his indiscretions during the marriage to ABC News' Barbara Walters in a 2008 interview.
"I realized that my needs hadn't been taken care of…And I took the cowardice way out," he told Walters. "I wanted a little acknowledgement, a little attention, a little thank you every now and then, for my efforts."