In my opinion...NO, do not push her to admit anything. If she's not ready to tell you about it, it will just make her avoid you (to avoid the chance of having it come out).

No, I didn't have a 1 night stand. It lasted many months.

The best thing you can do? Read the book The Five Love Languages by Chapman. Learn your wife's love language and start speaking it. Having been thru this, I can honestly tell you that an affair begins when you do not have your needs met. You just feel so low, and when someone makes you feel better about yourself you just gravitate towards him. You need to figure out what your wife is missing in your relationship. I am not at all saying this is your fault! She is being weak and taking the easy way out. You can get past this!
My H and I were High School sweethearts, too.

I will try to find time to look at your thread tomorrow to get a better feel for your story.