I mean, honestly, it just sounds like you don't like dogs which I totally get. The dog is just being a dog, and not everyone likes dogs or the things that come along with them (although people look at you like a monster if you say that, but if you say "I hate cats" people totally get you). I mean, I dislike dogs and I personally wouldn't even get into a relationship with someone who had one. Instant dealbreaker for me.

But, since he already has the dog and it's his pet, it'd be incredibly cruel for you to force him to get rid of it as it's basically like his kid, he's responsible for the dog and loves the dog. It's a commitment he's made. I think the ground rules you have are fine. Is it possible this is something additional training for the dog could improve? Though, it doesn't seem like the dog really has any behavioral issues.

I think you should remove yourself from the situation (break up with him), move out and keep separate housing or learn to live with the dog and figure out why you