The weekend mediation hearing "essentially ended their marriage," the source close to Kate tells PEOPLE

By Mike Fleeman
November 22, 2009 03:00 PM
Credit: Brian Prahl/Splash News Online

With lingering anger and bitterness, the marriage of Jon and Kate Gosselin is all but dissolved after Saturday’s all-day mediation hearing in Pennsylvania, a source close to Kate tells PEOPLE.

“This was the proceeding that essentially ended their marriage,” says the source.”Kate is just relieved that a very painful chapter of her life is nearly over, and she is looking forward to building a better, brighter future for herself and her kids.”

During the hearing, Jon “didn’t dispute Kate having primary custody of the kids,” says the source, which came as no surprise to Kate.

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Nor was she shocked when Jon showed up to the session with a bouquet of roses. His lawyer said they were a peace offering, but Kate saw it as something else and refused to take them.

“In what should have been their most serious moment as a couple,” says the source, “Jon again resorted to a publicity stunt.”