With a few 'tweaks' your DH and mine could be brothers, so I'll make a few edits.
"Lots of shouting, I’m the problem, <he doesn't have a drink problem> he drinks because I’m so miserable, because I emotionally abuse him. I’ve never done a days <housework> work in my life apparently, he’s had to do everything".
I always worked full time, earning the same or a little more and our pensions are about equal now that we're retired.
As far as housework, I'll admit you could never do brain surgery on my floors but the house was always clean. HE was the messy one with piles of magazines, papers, etc that I was forbidden to touch. Now that I've left, the house looks like a hoarder house and will need professional cleaning when that time comes.
When DH was served with the separation papers (legal sep works better financially for me at this point) he flat refused to contact an attorney believing (I think) that if he didn't respond nothing could happen. More the fool, him. The hearing is next month, he's been notified. My attorney says it's not on me if he's drinking too much and doesn't respond or show up and we need say nothing at the hearing. So if your DH thinks he can stop a divorce, let him. You move forward and let him be the one that has to play 'catch up' to you.
In our case the dog is 'ours' but more his as far as who the dog was more attached to. I didn't plan on taking him but DS2 called me shortly after I left and said I needed to have the dog because DH was so drunk all the time that he wasn't feeding him right and not taking him out regularly. DH ended up in the ER and I came and got the dog whilst he was gone. So at this point, the dog is 'mine'. It wasn't what I planned but it is emotional support and company. He's perfectly content with me and doesn't miss DH (as far as I can tell). DH berates me for 'stealing his dog' but it rolls off my back. I tell him I'd love nothing more than to share the dog but until he gets his act together, that's not going to happen. Dogs here are considered 'property' so 'possession is 9/10ths of the law' and there's nothing he can do.
Bottom line @LavenderFieldds is that you and I know the truth and that's all that matters, so hold that truth close to you. Let them scream and shout about our 'inadequacies' and what we supposedly can and can't do til the cows come home. It's all 'sound and fury, signifying nothing'. Take the steps that are right for you. And when you do, even if it's a small step, really feel your 'power' and every step to peace and freedom.
So yes, you are doing the right thing.