An emotional Christie Brinkley is fighting with ex-hubby Peter Cook in court today over the contents of their divorce case -- which Cook wants to keep private. "This is a family matter -- a private matter," said Cook, "and it should stay that way."

Brinkley's lawyers argue that the case needs to be open to the media -- to get a just verdict. "I've always hoped to settle these matters privately outside the courtroom," said a shaken Christie, "and continue to hope that'll be the case." Their divorce trial begins July 2.

The supermodel ended her ten-year marriage to her architect husband two years ago, after a cheating scandal involving Peter and an 18-year-old assistant. The couple has two children; Jack, 12, and Sailor, 9.