Just be honest: stepsister's been spreading some nasty false rumors, and you're just not comfortable sharing a roof with someone who would do that.  You're sorry this means missing out on time with Mom, and you don't want her to feel in the middle or like it's on her to resolve the situation (although if she is willing to talk to her husband about it, you'd be appreciative), but you hope she'll support you in doing what you need to do for your mental health.