You won't save your marriage by allowing him to see you as a doormat. You just delay the heartbreak and spread it out over a longer period.
People tend to value what they lose. Think about it: when have you felt more intensely for him? Choose for him. Choose your kids, choose yourself. Tell him he's had his chance and blown it. She's welcome to the booby prize he has shown himself to be.
You are better than this, OP. Make sure he knows it.
It is so hard with two young children who I want to have a whole family. How do I look them in the face if I don't do everything to save our marriage?
This is not in your hands. You are not the one doing anything: he is. The person who should struggle to look those children in the face is the man doing this to them, and to their primary carer. What is this push-me-pull-you doing to your capacity to care for the kids as a happy, secure person? He is the one harming them. Don't enable him.
He does not deserve the choice between you both! Who the hell does he think he is, and more importantly, who do YOU think you are, to be treated so badly?
Plan a lovely Christmas with your children and adults you can trust. Tell him you have had enough and don't want to see him until the New Year, and he can arrange contact with the kids via a third party. Arrange to do lovely things with your kids and your friends, and let him learn what life could be without his clear certainty that you're still his, should he want you. Let HIM worry about whether you are actually available to him for a change! What is the worst that can happen - he leaves, as he has threatened for months? Honestly, given his behaviour I wouldn't see that as a loss, but I also can't help but suspect you will be a lot more appealing if he thinks you aren't going to play his pick me dance any more.