You sound resolute, keep it that way...the hardest step is over, he needs to accept he does not live with you any more.
Glad he has somewhere to go so he is off your back.
Also very glad you are Ok I mean physically, emotionally this will be tough, it's horrible, but it's the only option.
Well done.
I remember ex being a bit ike this with me - loads of begging, empty promises, what did he do thatw as so bad etc...I needed someone there reminding me of it all so I didn't weaken, for a while.
But once you have made the decision in your head, and sort of 'unattached' from him, he becomes the enemy, he can't touch you or get through the wall inside your head.
Sounds as though you are well on the way to achieving this is you haven't done so already - it's very encouraging, you're doing so well.
It doesn't have to be awful forever, he'll get used to it, you can retain a vague sort of 'getting on' as long as he respects the boundaries, ie he does not live in your house, he doesn't even come in unless you say so, you never have to like him, or love him, or share anything with him again except maybe the children, a bit - whatever happens, you are two separate people and you are free.
Stay resolute and keep being the broken record, don't get into a discussion, don't justify it to him, just know in yourself he is not coming back and you'll be OK.
Losing respect for someone like this is very powerful and gives you a lot of strength to keep them away from you so they cannot continue to abuse and hurt you.
You got out before he injured you physically which is such a triumph.
Take it easy today x