TAPING of a new chat show starring Kate Gosselin was halted over the weekend when she broke down in tears over the pressure of her divorce on her eight kids. Kate began sobbing as she talked about being away from her children now that she and Jon share custody. A source on set told Page Six, “Producers flashed a picture of Kate’s children on a screen and she burst into tears. She said she hates being away from her children, but now that she’s to be divorced, she has to work to support them. She was very sad, emotional and very guarded.” Kate joined a panel including former “Early Show” anchor Rene Syler, Lee Woodruff (wife of anchor Bob) and host Paula Deen for filming at Chelsea Studios. The Telepictures show is conceived as “The View” for working moms.