Look, as far as you are concerned the fact that he is in the closet is irrelevant. You got involved with someone who was already committed to someone else. As much as he might have had a real connection to you and got a real thrill from being with you, the bottom line is that his family ultimately mean more to him than you do.
From your point of view, you should behave no differently just because you are gay and he is confused/living a lie than you should if this was a straightforward straight man/woman affair. Have some dignity, walk away, focus on meeting people who are free to give all of themselves to you, and who do not treat you like a dirty little secret.
From his point of view, there is a slim chance that he is bi and this is/was a one off affair not to be repeated, but I don't it very much. My guess is that eventually he will tell his wife or start to take so many risks because of his compulsion to sleep with men that he will get himself found out. It sounds as though his DP already suspects and she will be watching him like a hawk.
If she chooses to be in denial at the moment then leave her to it - that's her call. It doesn't matter whether he's with you or with another woman - if the children are young she may not feel up to being alone just yet, but the penny will drop eventually.
But that has to be HER decision to make - you don't get to make it for her. No good whatsoever can come of you trying to hurry things along, you'll just look spiteful and hysterical and he will hate you for it. Either way you are probably just a transitional relationship for him, on his way to accepting that he is gay. And when the shit does eventually hit the fan it is going to be very, very messy and traumatic indeed - 10 x as much as if he was having an affair with another woman. There are so many more layers of complication and pain for her with this scenario. Please don't bring this down on her and the children just to make yourself feel a bit better.