Hi OP.
As I said in my last post I've been in this situation with my ex partner except without children so I will make absolutely no comment on that aspect of your situation.
In my experience (and I say this to be honest and not cruel at all) he never changed. I've had apologies, I've had begging on his hands and knees, crying for me to stay and telling me he'll change or see someone for help but each and every time it was a lie.
Within a small amount of time he was back to being his abusive self and would often tell me that his apology was 'bullshit' because 'clearly he cares about this relationship more as he was willing to take the blame for a situation I'd caused so I wouldn't leave'. I'm not even joking, I got that every time.
They do not have the same logic as you or I. Trying to make them see things from your point of view will eventually fail because they cannot and will not accept blame or guilt. It is easier for them to push this on the other person and so that's what they do.
My expartner also had a rough up brining. His father was in prison for beating his mother when he was young. It must have been awful for him to witness that. I truly felt for him then and I feel for him now about it. But in honesty I grew tired of him using it as an excuse for his behaviour. He thought because he didn't physically harm me that he was better than his dad.
It's my view that these people cannot just simply admit their sins and then bingo all is solved, my partner need professional help which he refused to get and it was left to me to try and deal with his problems. I'm not a doctor I had no idea what to do to help him and that's honestly what I wanted to do at first!
But now I see that if someone honestly cared for you in that situation they would leave of their own accord and seek the help they need and come back to you a changed person and beg you for forgiveness.
My ex said he would do all these things when I eventually left him. And guess what... He didn't do a single one. His next girlfriend left him for the exact same reason I did.
These people are manipulative and they know exactly how to get you back where they want you when they have pushed things too far.
I really feel for your situation. It is confidence destroying and heartbreaking shit. I've been there. I've felt trapped and alone by it. Once I left and was on the outside of it I laughed at the fact I thought he was going to change. He didn't. Because only HE can decide to do that. I thought me leaving might give him the kick up the arse but it didn't because I don't have that power only he does. And surprise surprise he tells everyone the break up was 'out of blue and he doesn't know why I left'. He knows exactly why and he couldn't bare any one else to know because that would damage the perception he has of himself.
You asked for other people's experiences and this is my honest one. I've had moments like you where I've thought 'hes going to change, he's told me he will, he's admitted what he doing'. It never lasted.
I wish you the best in your situation whatever you decide xx