Colin and Alexis Gosselin, both 6, were indeed asked to leave, the source said, although not for bad behavior as has been rumored.
"The situation is being grossly overstated," the source said. "The kids are going through a challenging time, but Kate doesn't feel this is something that should be discussed publicly. It is a private matter."
Colin and Alexis are part of a set of sextuplets who, along with twins Mady and Cara, were the stars of the cable television series "Jon and Kate plus Eight." The series ended when Jon and Kate split up.
Kate Gosselin recently told PEOPLE that there have been some tough moments since the divorce but her brood in general are "amazing, resilient, loving kids."