I think you are absolutely correct to insist on being treated with respect. I am fond of saying to be treated at least as well as she would treat a stranger. I'm sure your wife does not go around treating strangers with the attitude you get at home. That is critical.
And yes, you do need to demand that she stop contacting OM. Although they all lie, so it is not that valuable a promise from most cheaters.
I wouldn't give up the MC so quickly. It is a place where you can communicate with a referee. It is likely to be more productive than trying to talk to her alone. But then I would have to judge that by my feeling at these sessions. Is the counselor making the situation fair to both people? Perhaps the counselor will have some other ideas of how the two of you can improve your homelife. I think a set time to talk about things is a good idea.
And I would let her know that if she cannot be civil to you and treat you with a modicum of respect, that the promise to not tell people, including the kids, about her affair is finished. They should know what is going on in their own family as it affects them as much as it affects you. And as adults, they may want to say what they think of the situation.
