This is completely normal OP and I have seen lots of similar posts before.
You've put up with 20 years of neglect, disinterest and what sounds like financial abuse from someone, who has ground you down so much you've become depressed, self harmed and lost weight. And now because he is spending some time with you and cooking twice a week you're supposed to switch off 20 years of hurt and difficult feelings off and suddenly feel happy? Minds don't work like that as if they did, people would get taken in by others too easily. Your mind is protecting itself. You need time - time to heal, time to see if he is being genuine, and time to decide if this is what you want.
If someone has been treated badly for so long, of course they're not going to turn round and feel all lovey dovey towards the person that's treated them badly. You have 20 years of evidence that he is not a nice person, why would you have loving feelings towards him? He also changed for selfish reasons, not because he realised he was behaving badly, not because you asked him, he changed because he didn't like you leaving and he didn't want to be single. I dont think 'good dad and involved parent' is really who he is, otherwise he wouldn't have ignored you all for so long.
What I'm trying to say is you have 20 years of evidence he is a shit person and you'd be mad to ignore that and a lot of the stuff he has done is unforgivable...so why should you forgive? I know you want to but it's a feeling that you can't force
A couple of other things.
You keep saying that your mental health is your responsibility. No. If youd had a perfect life and were still miserable then maybe but you've lived a horrible life because of him for so long, and are depressed as a result, how can it not be his fault? I really doubt you would feel this bad if you'd lived with a supportive partner. Maybe it's only you that can sort it out but that doesnt mean it's your fault. If he had hit you and broken your arm, it would be his fault and his responsibility but only you could do the physio to make you better. It sounds as though both you and him think he has been only a small part of the problem rather than the root cause.
And it's not always best for the children to stay. It doesnt benefit them having a mum who I suspect still does more of her share, who (rightly) resents their dad for all the shit he put her through and who is depressed because she feels she should live with him.
Be kind to yourself. He is home more - great, start doing things just for you. Go sit in a cafe and read a book or magazine. Go out for a walk or a swim. Start a hobby you've always wanted to do. Join a book group or something. Force yourself to do things and rediscover your own identity. See a counsellor and speak to your doctor about how you're feeling. Look into leaving again, can you manage this financially? If not what can you do about this? Do you work? Is there anything youd like to retrain in or do a course on? Don't feel guilty about planning to leave, even if you decide not to in the end it is sensible to have a back up plan in case