Well, you tell yourself that you now have even more proof that he's a filthy, manipulative liar. Snooping is only going to give you more proof of that and, honestly, no good will come from it.
Don't tell him that you know the latest. It doesn't matter. You are divorcing and the A was a deal breaker long before this idiot and his niece ever came along. If there was a chance at R or you were talking about it, then you would have to somehow let him know that you know he's full of shit. Since I don't see where R is anywhere near the table, don't bother. Liars lie and cheaters cheat.
None of the stuff that happens after the fact matters. It only hurts if you keep looking. Remember how you feel right now - pissed off, sad, confused - and keep thinking of that the next time you want to log on to see what he's been up to.
As far as the kids go, get them into counseling - they will need help navigating through his manipulation and you will need guidance on how to handle their moods when they come home. That's the only thing to do now - don't look to him to help you with any of this. Look to the outside - friends, family, SI, and professionals - he will only make all of this worse.
I'm sorry you're upset. It sucks. But, stick to NC and the matter at hand. Who he dates is irrelevant now, just like his empty words.