Sorry you're going through this op.
Have you supportive family?
How old are your little ones?
I'm asking partly as I'm wondering if you could take a few days away...maybe in the sun? Sometimes being able to leave everything behind for a few days can help us reset. If you could leave the kids with family maybe?
I mean you could also take them but don't let him know/block him for a few days so he can't bother you. Maybe don't tell anyone, just go.
A few days break might do you the world of good. Take a book and just relax by the pool somewhere.
That asside, have him blocked on everything bar one method of contact. A burner phone you can leave in the drawer and only check once per day perhaps? And then, never reply to him about anything other than the kids. And even then, step away for ten minutes before responding so ge can't goad you into knee jerk reactions.
Stay off social media so you aren't tempted to snoop. Tell your friends and family you neither want to hear anything about him or for them to tell him anything about you.
Cold turkey is best. But as you have kids this just isn't fully possible. Can you have relatives do any pick ups and drop offs so you don't need to see him? If not - keep them brief. Stay in your car. Don't go into his home or let him into yours. Look up the grey rock technique to help you handle time spent around him. It's basically about being boring and not giving him reactions or info about yourself.