I'm going to offer a few bits that vary from the eff him approach. The thread is a bit blurry between what you've actually posted, and reactions. Apologies if I've missed some key points that up-ends this.
DH and I experienced tremendous stress following the arrival of DS2. Every argument or bit of criticism escalated/descended quickly. Things broke, including my breast pump that I "dropped" in his general direction. It wasn't just me being hormonal, but DH had post-natal, and he was intolerably horrid. Fortunately he was willing to see a counsellor (recommended by an NHS doc) and I had two very sensible friends to support and disagree with me as appropriate. We are through the worst of it.
After time and counselling he returned to his good natured self, mostly. It's still not equitable at home, but he does just enough to show he cares for me and the boys. I haven't threatened to call a solicitor since DS2 was 5 months.
Household duties are not even - now or before. Or equitable. I'm the high earner. I didn't realise before marriage it would be so, but it is what it is.
I am trying to take a child-rearing strategy to DH. Micro skills. Or just nudging him a bit at a time. One meal per week is my current campaign (he can cook with his credit card or even spag bol). He wouldn't fathom frozen salmon unless it was from the Cook frozen food shop (which I highly recommend).
DH is almost operating at his full capacity, and it isn't fair for me to expect what isn't within that capacity. I have to help him increase his capacity before I can raise my expectations. He's a slow domestic learner - am sure DS1 (3yo) will learn to deal with frozen salmon ahead of DH.
I would state that DH did not generally criticise my household management. He valued to keep his head attached to his body - and me away from solicitors. During his PND time he was critical, but I did my best to let it wash over, and give it a bit of time to rebalance. Those first months are very challenging and they are not "normal". Your emotions are ever so valid, but don't let hormones and your or his PND make your long term decisions. Your frustrations won't change, but the degree to which you feel them will.
Agreed, if your home is owned per the Land Registry in the names of DILs, it is not on the table for division of marital assets. It costs £1-£2 to check if it is his or belongs to his parents. Financially you need to think about (and discuss as appropriate) your long term position. Was it Joan Rivers who advised to get everything in your name? If your debts are gone and reasons for those debts past, he has no reason not to include your name on the title.
Also to consider at the appropriate time is to use the government-paid 15-30 hours of childcare to take courses or seek experience that can upgrade your skills, so you have more choices available to you and DD.
We all wish you positive energies to make the best decision for yourself and DD.