Hey there. I'm glad that you found us for support.
His relationship with his kids is his problem. He created this mess, it's not up to you to try to fix it. He fired you from being his wife. He no longer gets any of the benefits, including you trying to mediate between the children and him.
How do you act? As if you are doing business with a business associate who is rather a jerk. Polite, to the point, discussions of finances and children only. Nothing else. He gets no comfort from you, no support, nothing but disinterested and dispassionate business discussions. Then you call it a day and walk away. Remember. He fired you from being his wife. You don't stay chummy with the man/company who fired you unfairly. You do your business and then leave them in the dust.
Frankly, if/when people ask how you are, you can have several answers. For strangers and not close acquaintances, "fine, thank you, and you?" will work just fine. For anyone that you are close to, "as well as can be expected," might be in order. Only with your close friends/family, who have your back completely, would I personally go any deeper than that. Remember, YOU did nothing wrong. Keep your self dignity and respect. Don't give other people ammo because of their prurient curiosity.
Come back often for support. We're all here for you! (((hugs)))