I am very sorry about your sitch. I did the same thing to my W. I wanted to believe her that the R with the om was over. I wanted that we stay together. But I have to accept the fact that my W does not want to give the om up. SO the only way is that she moves out.
Your H is the one who is having an A, so he has to move out. Not you.
I am preparing to have a settlement that could go nasty if she is listening the the om. But it is life.
I can understand your feeling of betrayal. It is your decision about what you would accept or not accept. You can ask a trusted friend to call the number of your H's cellphone if you want to confirm who she is. Just pretend that your friend has dialed a wrong number.
I find more peaceful now. Not worrying whether my W is doing behind my back. I have to move on with my life. Pray to God to grant you peace also.