I can relate to his frustration, though. When my husband and I were dating and moved in together, he (of course) brought his dog. The dog growled at me, tried to bite me, went through trash, pissed indoors even moments after a walk while making eye contact with me, etc. At first I chalked it up to an adjustment period - he was used to living with only my husband and now had a new human and my cat to get used to, plus a new environment.
But it didn't get better. When he'd make a mess or destroy things or piss right in front of me right after going for a walk, I would do what my parents always did with our dogs - I would lead him to the mess, say "no" firmly but calmly, and tell him to go lie down in his dog bed like a doggy time out. My husband insisted that training him would do no good so why bother, disciplining him like I just described only made the dog sad, etc. VERY ANNOYING.
When I was pregnant the dog tried to bite me. I asked my husband what he was going to do about that behavior since we can't have it around a newborn. He said that if the dog ever showed signs of aggression toward the baby he would be GONE. Guess what, didn't happen. I spend most of my day on edge trying to keep the dog and toddler separated because he has growled at her unprovoked, tried to steal food from her hands and nearly bit her in the process, and once LUNGED at her from across the room with no provocation while she was sitting on my husband's lap.
That was two months ago and I gave my husband the option of either finding a dog behaviorist and making time to work on the issues with his dog, or finding a child-free home for him. He again said training was stupid/wouldn't work and he would rehome the dog - didn't happen. I have brought it up several more times, said he HAS to do something because it is not fair to anyone for us to all be afraid of the dog or for him to be locked up all day when we're home. NOTHING. It's very similar to OP's situation, except we already have a kid now, but it's a tough situation to be in as the non-dog-owning partner. I can't demand he rehome the dog or he will resent me and I will feel like a shitty person. I can't train the dog without his help, and he refuses to do it. I can't keep being afraid this dog is going to "accidentally" bite my kid. It isn't because either of us is immature, it's because the dog owner doesn't see the issues as clearly as the other partner; they think maybe we just hate the dog or are jealous or whatever, instead of accepting that the dog needs to be trained. It sucks.