Ummmm....yeah.....why DOES it sting? You certainly don't want his sorry A$$ anymore. And as galling as it must be to contemplate him marrying the OW, doesn't it also kind of tickle you a little - to know he's creating his own punishment here on earth?
I mean - would you honestly feel any better about it if he dumped her and took up with some hot woman stockbroker???
As for the bill stuff - make sure YOU pay YOUR share directly to whomever, and keep a receipt. That way you'll also have your cancelled check or credit card statements as well. Keep a file with all those things. Once a month you can email an accounting to your ex, including everything extra you've paid for the kids; he can then email it back, amended for the extras he's paid for. That's how my ex and I handled it. One of us would then pay the other whatever overages were owed.
Your ex is not so smart and needs to see it spelled out in black and white. Sorry but you'll have to be the one to do the accounting.