H and OW are almost certainly in contact. If not, he'd tell you that he very clearly put an end to contact. Instead, he is saying that he doesn't understand why talking to her is a problem.
What is the possibility of one of them changing jobs? Is it possible for him to completely avoid seeing her/speaking to her at work?
Disrespecting you and your family, not putting his family first, not clearly ending things with OW, continuing to act like OW's friend is being a jerk.
Politely and firmly and clearly stopping all contact with OW in a transparent way is not being a jerk.
OW engaged sexually with a married man who has returned to his family. It is unreasonable for her to expect him to continue to act like a friend toward her. It is not mean to end contact. It is the best thing for everyone. So, if H wants to be a decent guy and not a jerk, that is the thing for him to do.
In your place, I'd first try some compassion -- it must be very hard for him to end that R, very painful, and he doesn't want to hurt anyone. But it is not being a jerk to firmly end an inappropriate R that hurts his family.
Then I'd set a clear boundary. I'd tell him his R with OW at any level does not work for you and you will not accept it. She is not a friend to your M, the two of them had an inappropriate sexual relationship and an emotional affair. It is time for all contact to be stopped in a transparent manner. His job is to find a way to do that without being a jerk.
But, only set that boundary if you mean it.
And, don't doubt your intuition, it is probably right.
