I am so sorry you are dealing with all of this.
I read this and you are being extremely harsh on yourself. I haven't ever had children but I know depression is real, and I know that post natal depression is real too, they are not excuses, they are genuine mental health issues that nobody would choose to have.
So I am 8 months out of an emotionally abusive engagement to someone who treated me like dirt and I learned quite a few things after I left.
Normally you end up with peole like this because you are vulnerable, and you certainly were very vulnerable when you met him. He was better than your last partner so you probably overlooked a lot of things that were red flags at the start.
You also had the belief that your daughter should have a father, probably becasue that is what you always envisaged and nobody can blame you for that at all - you want the best for your daughter and that is often the "traditional" family.
I understand the idea of not being able to accept your relationship ending, I felt so very much the same - I tolerated so much becasue I couldn't handle the idea of it not being a forever thing and I told myself it was all in my head, or not that bad etc. The bottom line here is how you feel, and also how your daughter feels. You can see that this isn't right and I urge you to stay with that thought process because you are dead right, it isn't right at all.
Also understand that he goes through phases of being better, and this is confusing as hell as I found because if they're nice and better for a period of time you blame yourself and wonder did you ever experience what you thought you did or where you blowing it out of proportion. The answer is no you weren't, and intermittent reinforcement/inconsistent behaviour is addictive on the brain - like a slot machine - will I "win" today? Win being - will he be nice to me today? Will I be approved of today? Will he be nice to DD today? It really affects your ability to leave because it is not "all bad" and it messes with your head. I think that is the biggest challenge I had. My ex would cook for me, I hated cooking and he cooked amazing dinners and I thought "well he must care about me then".
At the end of it all though, them being "nice" or "good" for a while doesn't take away from the sheer misery they cause when they are "not good" and they are frankly abusive and vile. There is no excuse for that, ever. One does not directly cancel the other out.
You are living at the whim of someones moods, what THEY decide your day is going to be like today, how THEY decide you're going to be made to feel today. So is your daugther. None of it is ok, that is not something anyone is entitled to do to you, the only person who decides how you feel is you. To add to this, she is not even his daughter, and to be honest I would start to get your ducks in a row and consider how you are going to seperate. I don't say it lightly because I know that it's easy to say "dump" online, but at the same time you and your daughter are being made to feel like absolute shit any time this man decides and you know something? You can have an amazing life together without him making your day awful.
I went through so much anxiety, so much "how do I be better" - i even spend hundreds on a dating coach who claimed she could "help you bring out the best in your man". I'm not saying I was never the issue but bottom line - he was the issue, he would pick fights, dismiss me, insult me, shout at me and swear at me.
The only thing I wished I'd been able to do that I didn't do was to react calmly and not take it personally, I wish I'd just looked at him with the utter disdain he deserves and asked him "are you done yet" and been able to be unaffected by his shitty behaviour. Easy to say when you're not in it though!