Peter Cook has quietly married his longtime girlfriend Suzanne Shaw and says he kept the wedding a secret from his ex-wife Christie Brinkley for fear that “Christie would drag it into her black hole of revenge and hate like she does everything else good in my life.” We can reveal that Cook secretly wed Shaw last Valentine’s Day in a sunset ceremony in the Hamptons before only close friends and family. But they kept their nuptials hidden from the public. “I did not want to openly share this happy moment in our lives,” Cook, who is in a bitter custody battle with Brinkley, told The Post’s Selim Algar. Cook began dating single mom Shaw soon after his 2008 split with the Uptown Girl. Cook and Brinkley are due in a Long Island courtroom tomorrow in an ongoing battle over claims of harassment, and money squabbles, relating to their two kids. Cook also claims Brinkley has shut off communication between him and his kids, and bars him from decision-making related to them. Suffolk County Judge Mark Cohen has ordered both parties to show up in person in an attempt to avoid another round of warfare. But sources say both sides are dug in. “We’re still significantly far apart,” Cook’s lawyer James Winkler said. Despite having no contact for two years, Brinkley and Cook accuse each other of violating a “civil communication” clause in their settlement through hostile e-mails. Also, each side wants compensation for a few thousand dollars they allegedly owe each other for the kids’ schooling and medical care. Cook said his goal is to have the judge appoint a “parenting coordinator,” which he claims Brinkley has refused. Brinkley’s lawyer Tom Campagna did not return calls for comment.