I doubt this will be helpful, especially since you have young kids, but when things started going south for us, W bought a dog. I made it absolutely clear that I wasn't taking care of it in any way, shape, or form. "Oh, don't worry, we (W and kids) love this dog and we'll take care of it!" But no one did. The only thing I would do is fill its water bowl because I felt sorry for it. It was so bad that I literally walked around an obvious steaming pile of $hit in our hallway for a week before someone else cleaned it up. After that, I think W got the message that it was her responsibility, not mine, and things got better. Yes, it was passive/aggressive, but I didn't go that route until more traditional methods failed, so I did something different.
If you just stopped taking care of this dog, what would happen?
BTW, with small kids, I wouldn't recommend leaving poop lying around, but maybe put it in his car with a note explaining why?
M:23 T:26 Me:53, Wife: 60 S:18 D:16 filed 7/16 W moved out 4/28/17