Stay silent. That is your answer for everything. Have a backup for the child care if he doesn't come through but don't talk about it to him. Avoid at all costs making excuses to contact him "for the children." If they are sick, take care of it. If you need something from the store, get it yourself. If you need childcare, arrange it on your own unless he initiates it and volunteers. Only contact him about a real emergency (kid or you in the hospital) or if he messes with money that you need. Do not ask him when or where he is moving. Do not ask him where he is going or with who. Do not mention any other women. Block him on FB for your own sanity. Stop snooping, it is for you and not him.
He wants his space. Show him what that really feels like. Make him feel exactly what it is to be divorced. Mentally treat him like your ex-husband. See how he likes it and whether it causes him to cycle in. If he does, stay cool and wait it out.
When you start doing this you will detach. The pain will absolutely lessen. Your relationship with him will improve because every interaction between the two of you won't be a relationship argument.
Take it day by day. Resolve to get only through today not contacting him. When you accomplish that, wake up tomorrow and do the same thing. If you feel like calling or texting him write on here and me or someone else will tell you not to do it.
Do not even think for one second in your mind that you will take him back unless the person in front of you has shown by his action that he is the man you love. No more promises about trying. No coming back for the kids.
One day at a time TO and if that is too much, then one hour at a time.