I can only answer regarding the final break-up. H initiated it and took steps to insure she could not contact him again.
I do know she "broke up" on the day I discovered the affair. She was with H when he discovered that I discovered the affair. She was terrified I would contact her or her husband. I'm certain she used this to emotionally manipulate H. I must admit to some evil pleasure knowing that she was concerned about my knowledge and how I would use it. That break up didn't last. I don't know who initiated it the second time H told me it was over. I think it was H based upon things he has since told me. I think OW emotionally manipulated H and pestered him a lot at that time. HB "saw" that, and I saw some evidence of her contacting H shortly after H told me it was done the second time. (she had the nerve to comment on some family vacation photos on H's facebook) I wasn't snooping. It was right there for me to see. I ignored this at that time as that was what I was told to do, and what I decided was the right course.