Christie Brinkley and Peter Cook's bitter split escalated Thursday when the two squared off in a Long Island courtroom over whether to keep their upcoming divorce trial open to the public. Brinkley's lawyers requested to keep the courtroom open for the trial while Cook's lawyers argued to keep the bulk of the proceedings closed. The law guardian for the children, Theresa Mari, petitioned the judge to close part of the trial to protect Jack, 12, and Sailor, 9. The trial, set to begin July 2, is expected to be explosive, with reports surfacing that Brinkley's side may reveal Cook's alleged interest in Internet porn and swinger sites. Divorce trials in New York State are open to the public unless a judge decides to close them.