You didn't cause this. It's not your fault. You are being victimized.
Your husband should have put an end to this pretending that you do not exist. If he doesn't understand why it's happening then he is not paying attention. Perhaps he does understand and he doesn't have the spine to stand up for you. Regardless of understanding, he should not allow it to go on.
Grief is a weird thing, but he sought comfort in a person he never should have sought comfort from; your absence at that moment did Not make him do that. He chose to do that. The proper person would have been you and/or a counselor.
I'm sorry you are going through this. I know it's alot but I'd consider changing to a new counselor if I were in your position. Your current person does not seem to have very viable solutions here. I would not hug a woman my husband was having an affair with either. No thanks.