Have you ever tried allowing W to have the dog even for one day? You really don't know until it has been tried.
Has W had the kids over too? I mean...do you see it at all?
Your so-called logic has me baffled. Just doesn't make any sense to me at all. Your W knows that the dog has medical issues. Who's to say that her place isn't any better than yours? Dogs really don't care where they sleep as long as it is a warm place.
To answer ... yes, she has come over and taken the dog he is about 100lbs and she is not to far from that, he pulls her where ever he would like to go. Like I said ... no decision needs to be made today, I am suspect of how sincere she is at the moment (Given the history her mind will change in 24 hours), her place does not allow dogs.