He says no PA, you say letter suggests PA... I feel your pain and don't want to be vulgar, but did the letter really indicate intercourse or similar PA...
Of course, believe nothing of what he says and 50% of what he does...
He indicated in the letter that he does not want to leave you because of the kids. OK, that's a start.
Or maybe is he trying to end the A and that's his excuse to her?
I understand it's hard to talk to him right now and best to take a bit of a breather for you.
But if you've had "the talk"... what is he saying to you? Is he staying with you? Does he know what he wants? Does he still love you (regardless of staying with you because of the kids)...???