Only just catching up, but seems to me the OP got a variety of answers - which is pretty much par for the course on MN, anywhere.
Then - and only then - the thread deviated, and I do think its very likely that recent events have cast a long shadow over certain reactions in that part of the thread.
Either way - OP, if you are still reading this, and FWIW, I totally understand the struggle and if your own psychological or physical health and ability to cope are in question, that comes before anything else: if we can't take care of ourselves, we can't take care of our dogs or our children or anything else.
That said, it also sounds to me as though your ex has put you under pressure - and that you are understandably angry with him for dropping responsibilities (for whatever reason) eg walking/looking after the dog all day long. I do wonder if the dog has become a bit of a hot potato, metaphorically speaking, between you and your ex....and sadly, pets (like children in other cases sometimes) can become just that when families break up
I'm definitely not saying that as a judgement, either - just a fact, and something thats maybe worth thinking about if you haven't already. In order not to do anything you may regret in a year or two, that is.
I think your dd is probably a very, very small part of the whole dynamic here...personally, my guess is she'd be fine either way, as long as her parents are fine. Its very hard not to put things on to children that we feel ourselves, IME. Whether the dog would be fine re-homed is another question altogether. I hear you trying to do that carefully and responsibly, and yes of course it would still be traumatic for him - but if you do go ahead and re-home, keeping him with you until he can go directly to his new home, and making sure they promise to contact the rescue/you if they ever had problems and couldn't keep him, is the right way to go.
Break ups have so much fall-out
, I wish you luck with it all.
As for DogHouse people all being zealots and wrongly prioritized nutcases
um, no. Reactive nonsense.