Oh Stella!!! This woman sucks!!!! She is taking advantage of your confused and coward H. She is so manipulative!!! OMG, what a looser she is. Playing the victim here!! You have her number? I could easily give her a piece of my mind...
On a positive note, your H is telling you the truth. And just like you said, it must be very embarassing for him. So, he is trying to be straight with you. And I would even go as far and tell you he is asking your help in a way. This is time for planning a strategy. I wish I could have some advice to offer about it. I am just not sure that going dark is the best approach right now. He needs to see what she is doing and realise she is using his guilt to attract her back to him. What a low life...
I am sorry. Although recently I am not feeling very compassionate about our Hs, I really believe your H is trying and you must somehow reward and help him come through.