I agree with you, and it does sound as if it is a batyle of the houses, the best thing for you to do is continue to let her stay in her own room and if she complains of nightmares dont make an issue of it, it is possibly she is trying to get more attention, so dont give it for these issues , feeding into it makes it worse, instead try to make her stay with you one that she will enjoy,, get her doing games and outside Fun, activities, be clever fill her time with you with pleasure, and she will want to be there and let her Mom say what she likes ,its your time with her make it a fun time and not dwell on negativities, if she complains let her , shrug it off. Focus on her positive side.Let her Mom worry about the showers .
PS You are correct about the TV make sure she has a lot of nice books instead to read, and read to her before bed and anytime, reading is the best thing for her.