Hi Op, I'm afraid I agree with other posters, this man won't change.
I could have written your posts as my ex behaved in an almost identical way to your H. I stayed in order to keep my family together too, I didn't believe my little girl was affected by my relationship because I put on a good act and kept everything away from her. It was only after moving into refuge and seeing her blossom into a happy, relaxed and confident child, from the very first day in fact, that I realised how much she had been affected by everything.
It was unavoidable really when I think back as I was living half a life, I was emotionally drained and battered, even though I planted a smile on my face and tried my best to be a happy and attentive mummy I didn't really succeed, because everything I was going through dominated my mind, it changed me.
Once in refuge my daughter started asking me questions about things she had heard, she had been in bed but heard him shouting and sometimes smashing things. She was only seven but she had this need to understand. For a few weeks after we left he tried to talk me into going back and she would whisper in my ear "You aren't going to love daddy again are you mummy" or "We aren't going to move back into daddys house are we mummy." She kept me strong and she kept me focussed, not once did she cry or ask for him. His abuse intensified when I was pregnant so she had grown up with it, it was all she knew, sad mummy and angry daddy.
I used to use his childhood as an excuse for his behaviour as it was less than ideal but, the truth is, he is a grown man, responsible for his own actions, his childhood didn't force him to be an abusive twat, he made that choice himself. What kind of a man wants to inflict the same kind of childhood on his own children that his own parents forced him to endure?
Me and DD have a wonderful life now, almost four years after leaving, abuse free, a life full of fun and laughter, leaving was the best thing I did. I spent far too long trying to understand him, I spent a small fortune on books trying to find a way to cope, a way to live with him. My advice to you OP, cut your losses and leave. Save yourself and your children because you can't save him. You and your children deserve a far better life than the one you are living.