I agree with the others that you should stop paying the utilities but definitely give her notice.

I have to say as a breast feeding mother of a 20 mnth old that DS still feeds 2/3 times overnight which would make it difficult for overnight visits. DP has looked after him all night once and settled him with milk and had to sleep with him and I am going away in a couple of weeks and I am very nervous and I am with my partner. What I am trying to say that while you shouldn't have to 'prove' that you can look after DD overnight it might go a long way to help your cause to tell her how you would handle an overnight visit. Hope that makes sense...

I would also be talking with a lawyer to see what your rites are and if you aren't happy with your current lawyer find one you are happy with