Perhaps your wife is struggling because you have not told her the entire truth. My H confessed to a one night stand. I was willing to forgive him but I had a nagging feeling there was more to the story. I told him I wanted to know everything and if I found out more later I would leave. Well I found out more later. We are now divorced.
I can't tell you what to do but I will tell you that your wife is going to have a very hard time trusting you again. She is already aware of the EA but having the double whammy of finding out that it was really a PA and that you lied about will be hard for her to take. My feeling was if my H lied about his A just being a one night stand and then I found out it was more, what else was he lying about? Now I wonder how many more there were. There may have not been more but I don't believe anything he says anymore.
You have gotten yourself into a bad position. No matter what you do there are going to be problems and you seem to have the attitude that your wife should just get over it. It takes a LONG time to get over betrayal. A very very long time. It will take a lot of patience on your part. The burden of repairing the marriage is going to fall into your lap. She is going to cry and question and its going to happen a lot.
