What do I do if my 16 year old child refuses to leave her dad's house on the week I have custody?

I think you need her fathers help to open up for communication here. Also find out why she wont leave. maybe she has plans. At that age parents need to accept that the child also have a life and plans of their own. No child likes to live one week here and one week there and maybe you can switch weeks. Let her have a say in it, it affects her life more then any of yours. Maybe you can skip this week and spend that week having lunch or something with her and find out the reason she wanted to stay or the reason she didn't want to go to you. There are tons of things going on in a 16yo girls life most parents doesn't have a clue about. Calling the police or something will not help the situation with you daughter. She will most likely get very angry and then you will have no chance to speak to her.