My question to you is, "is there a timeline on signing the papers?" You no longer have to do anything for your STBXW, unless required. You do not need to sign the papers just to satisfy her. She tries to play hard ball when it favors her, but then "sucks up" to you if she feels it may favor her....ie...sleeping over. You need to drop the rope, stop letting her pull your strings. You do not need to reply to any texts, emails, answer calls, that you do not want to. If you want to stop fighting, I completely understand, I was in a similar place. It was good to for me to stop, it allowed me to move on with no more regrets. I put in all I could, and once I realized it was a losing battle, I agreed and we ended it. I was fighting for something I thought would be best, but in the end I finally came to the conclusion that XW was now making my life very unhappy, and I no longer wanted that.
