Quote: Ok, I believe you and if you are truly just friends then I guess I don't mind if you talk to eachother...
LIAR.
Yes, Liar.
Why would you lie to H about something this important? Why would you turn down his offer not to talk to her?
How about: "H, boy, I really blew it today when I said it was OK with me for you to talk to her. It is not OK. I really appreciate your caring offer today to not talk to her anymore. I think I will take you up on that. Right now my understanding is that you have promised not to talk to her. That really means alot to me. Just so we are clear, is that your understanding too?"
Or, how about: "H, I am so glad that you and OW are just friends. But, I really am not OK with you talking to her as your R with OW caused harm to our R. What I need is for you to either not talk to her (as you suggested earlier) or for her to be OUR friend. If she can't be a friend to us and our M, then she should have no place in either of our lives. That is a boundary I have with respect to anyone either of us knows."
In any case, stop lying to yourself and to H about this.