My guess is that her kids mistreat yours because no grown-up has told them that the smackdown is unacceptable. Since this is family, and they're with you forever, you have to change that. This holiday, the moment someone steps out of line, you correct the offender(s): "It's not polite to snatch toys/hit/chase anyone. Play nice, or I'm going to tell your mother, and Lisa won't be playing with you today." If things persist, tell Mom that her kids are being a little too rough and that you're going to have your daughter play quietly in the room with you. That ought to go a long way toward getting her to acknowledge the situation. After all, no matter how tasty the turkey, it's not worth sitting around watching your child get punked.
Ask Mom Squad expert Denene Millner your questions at Parenting.com/momsquad.