Hi OP - it sounds like your inability to act is part of a 'freeze or friend' response which is actually the female version of the fight or flight response when phased with a physical threat. I only found out about this recently but it makes total sense: most women would struggle to outfight or outrun a male aggressor so our defence mechanisms make us more inclined to freeze (i.e. avoid doing anything to provoke an attack) or friend (i.e. behave in a friendly way to them so they are less inclined to attack).
Your experiences in life have taught you that, for your own immediate survival, you should avoid confrontation. And that kept you safe in your previous abusive relationship. But it's not keeping you safe any more and it's terribly harmful to your children. So you need to move beyond that.
It sounds like you're waiting to feel emotionally ready to face the confrontation. But the cost is too high for you to wait and you may never feel ready. So the thing to do is assemble the necessary support so you can go through with the necessary confrontation.
Perhaps the following ideas may help?
You don't owe him any explanation or discussion around this and he may become dangerous if you do. Your priority is to protect yourself and your DCs.
Ring the police and let them know that you are going to be evicting your partner and there has been domestic abuse and you are concerned things may kick off so you are forewarning them. Hopefully, that way they can respond quickly if need be.
Do you have any large male relatives or friends who can come to the house and assist you (and perhaps stay with you for a while afterwards)? I don't mean physically throw your partner out but be there during the process of him leaving. Men like him tend to be happy to bully women and children think but they are less inclined to bully men, particularly men who are physically imposing. If you don't have any large men to call on, at least involve some female relatives and friends - safety in numbers. He won't be able to bully 3 or 4 of you in one go.
Does he go out much? If so, get your support team round while he's out. Pack up his stuff and have it ready for him to pick up on his return. Even better, if you can, have a locksmith ready to change the locks so that his key no longer works. He will find somewhere else to go - he's an adult - he can house himself. He can sofa surf for a while if need be.
If he never goes out, get your support team round - tell him he has 1 hour to pack up his stuff and then he needs to be gone. You don't have to put the support team in a directly confrontational situation with him if you don't want to - they can just be there in the background ready to step forward if you need it.
I suspect you won't feel emotionally ready to do this before you do it. You are going to be afraid of what will happen. So just accept that you will feel fear but act anyway. Just make sure you have the necessary support available (police/relatives/friends) so that you feel protected during the process and in the aftermath.