OP you are behaving with grace, dignity and above all - rational and clear headed thinking. Your future and your children's future will all benefit from the way you are dealing with this. I am so impressed.
As for
"Can't we get past this for the children?" - even the phrasing is making my blood boil? "Can't we?" suggests that he is, under duress, willing to put it behind him if you will. What. The. Actual. Fuck.
I would be so tempted to reply
"Can you un-fuck your mistress? No? Ahhh shame. In which case, no".
But I am not as dignified or restrained as you. You keep doing you because you are amazing.