John,
If you want your marriage to work you must stop trying to get her to admit guilt for the affair or abandoning the kids. She will run for the hills.
You must forgive her and never bring it up again unless it is bought up by her in counseling.
Don't you see the tremendous burden of guilt she must be carrying?
That everyone knows what she did and will always be in the back of everyone's mind?

Let me tell you a story. When I was around 5 or 6, my mother left my father for a guy. I remember my mother bringing me around him, him trying to give me things and I just wanted nothing to do with him. My father demanded she come home.
After awhile she did. My father handled it with her and then dropped it.
Now, years later, as a matter of fact 2 summers ago my folks saw this guy at a car show. My dad commented to my mother that it was the guy she had fooled around on him with long ago.
You know what? My mother denied it.
Said she did not know who the guy was, would not even admit she knew him.

After all these years she has erased the pain she caused our family from her mind. It never happened. Easier for her to deal with then admitting she screwed up.
My parents have been together 30+ pretty unhappy years but still together.
Can you handle if she just wants to forget it? Can your family and kids do that?
Or will you all look down on her for her sin?
Put your self in her shoes.
If your deciding to forgive her then do it.
If you can't handle it let her go.
Rondo