Seems that W is still "playing" both sides and on and on. Still sees you as the back-up option. What would you like to do here? From my perspective, I think it's nigh time for you to put in LRT and stick to it. If possible, get a L and have W communicate with L directly on any matters related to the house and the dog. If you cannot afford a L, then have a trusted third-party to act as a go-between person.
Take yourself out of the picture completely otherwise W will not be able to feel the full force of her choice and its consequences.
