H: Thanks for coming by to walk the dog. While it was a thoughtful and appreciated gesture I have made alternate arrangements to have the dog tended to on Thursdays.

See, right now your H has ZERO sense of loss. There is no guarantee he ever will but either way you need to begin to operate as your own woman now. And part of being your own woman is safeguarding your finances, ensuring your home is not being used as a flop house and making arrangements for the care of your pets.

Would you allow a friend to use your home as a potential meeting spot for an afternoon roll in the hay? I doubt it. Why would you give your H the leeway to do so?