After our second (a DD) came along, my DH was useless. Some of it was down to the fact that DD wouldn't take a bottle and so was attached to me at all times which made it difficult for him to bond with her, but he responded by distancing himself and doing even less than he had done previously (which wasn't a lot). I was struggling too - DD didn't sleep and because only I could feed her I was overwhelmed. Meanwhile, DH was doing the bare minimum with our eldest (DS) - at one point I found out he hadn't brushed DS's teeth in six months!
I think what happened was that, given the stressful situation, DH felt lost and fell back on the model he got from his parents, which was his mother doing everything and his father working and then being a lazy arsehole. There were rows, but it all came to a head when DH very deliberately prioritised his work over mine, making it clear that he expected me to make all the sacrifices where he had to make none. It was so blatant it was actually quite helpful as he couldn't deny it. I lost it and said I'd had enough and said I wanted a divorce. One of the key things I said to him at the time was that if we split his life would get harder and mine would get easier, which said everything that needed to be said about the relationship.
What made the difference was that he could see I was serious about wanting a divorce. I pointed out to him (and he eventually accepted) the fact that he didn't bother listening to me until he stood to lose something, which is pretty shit. Over the following months, he tried various things to change my mind - big gestures, declarations of love etc. At one point he decided, with very bad grace, to 'take over' all the housework, presumably to make some sort of point. Of course, when he was doing housework I had to look after the children - he would never do it with a toddler and baby hanging off him, like I did. He huffed and puffed and complained endlessly about everything he was doing. I found it hilarious tbh - I nodded and smiled every time he mentioned the heroic work he was doing. Then, after two weeks, he just stopped. When I asked him about it he said - I kid you not - 'I've done the housework,' as though two weeks was enough and it was somehow finished. I think even at that point he knew how stupid he was being. He just couldn't admit that it was far harder than he expected and he regretted ever starting.
After being a massive baby about all that, he then came to me and said, yes, he could see the issue and yes, he was willing to change, but I would have to help him. I said 'Of course, I'll give you exactly the same amount of help you've given me. How about that?' - that amount being zero (or less than zero given that he'd made work for me). I also said that coming to me and saying he'd change but that it would involve me doing even more work was beyond arrogant and that, basically, he could fuck off. When he suggested couples counselling, I said, truthfully, that I am an excellent partner and do not need counselling, but if he needed it, he could go and get it.
Lo and behold he did go to a counsellor and she was some sort of magician. I think she helped him address some of the unhelpful ideas he had from his own childhood, which, because he is fundamentally a kind person, made him realise what a shithead he was being. The upshot is that about 10 years later we are still married and he is fabulous - he does far more than I do and at times I feel guilty about being the useless one. Our relationship is great - there's no resentment, pettiness, annoyances, whatever. We are a team.
With childcare and housework it's easy to get bogged down in details - who does what, standards etc. but underneath that there's something more fundamental around feeling cared for, seen and supported. If you spend time making a kitchen sparkle and then someone messes it up and doesn't clean it, it feels disrespectful, as though they just don't care about you, your effort or your time. It seems small but it really isn't - over time 'small' things like this corrode and corrode the relationship until you look at the person and feel they must hate you, or a least not like you very much. They themselves become an annoyance. No one wants to be seen that way.
I think you need to really honest about the fact that you're considering ending the relationship. Don't let him make you feel you're overreacting - you are not. The really frustrating thing is, solving this problem can lead to a genuinely massive improvement in your relationship, for both of you. DH has said numerous times that he is far happier now than he ever was previously, even though on paper he is a lot busier. He's not another child for me to deal with. He can respect himself as a partner and a father. He likes being involved - he's bloody good at it. The kids have huge respect for him and know they can rely on him. I think he's the best, which of course has a positive impact on our relationship :) It is worth trying to fix this, but your DH has to be on board. Making him see the need might be the hardest step.