First things first, my man...YOU are not to blame one bit for her transgression.
Second, you need to decide what you want to do. Is this a deal breaker...something that you'd be prepared to leave your wife of 35 years for?
To answer that, you're going to have to ask her some difficult questions and be aware of the possibility that she may lie to you.
At this stage, you are the one who truly gets to decide what happens. She is the one who went outside the marriage. You did not. She is the one who needs to do the "heavy lifting" regarding repairing what she has done...and that includes repairing her broken self.
You need to ask why she did this and if she has ever done it before. You need to tell her that the truth is the only thing that you will accept and be prepared for any answers she gives. Again, be leery that wayward spouses WILL lie. Not to simply lie, but to minimize...be it damage control or to not "hurt your feelings".
Sorry you're here, man. It ain't the best club to be in, but you'll hear from a lot of us who have been through this crap.
The biggest mistake you can make is begging and crying for the marriage.
Now your WW needs to see that you are confident in letting her go. Even though you don't want her to leave she must have the perception that her behavior is unexceptable.
Tough love approach is the only way.
In the mean time take the time to figure out what you really want, just don't let her know, as for as your concerned she can leave now.
Do not stand for anything less if she is confussed then she can leave and figure it out. If she is unsure what she wants then ask her to leave until she figures it out.
Enless she feels some real consequences for this behavior she will continue.
If you are pretending to be confident and strong...even though you are not she will not second guess her choices. Your tough love approuch will get her to think twice in what she is about to loss if she continues.
Now is not the time to be a nice guy who is apologizing for your adultorous wifes behavior. Now is the time to show your wife you command respect and will not tolorate sharing his wife.
Once you get her realling and the power shifts to her chacing you to keep her marriage then you can make the tough dicision to keep her around.
I met him two days later because he stopped at her work to say goodbye on his way out of state and I happened to be there at that time. I 55 years old and my wife is 51.
This guy just had sex with your wife in a van and you let him say goodbye to her? Boy he must have been laughing all the way out of town.
She shows no remorse, blame shifts saying you were not giving her enough attention, and you make excuses for her and say that it is that time in life?
You are so beta she was looking for some alpha sex. You need to man up right now. You need to be willing to dump her right now, maybe taking her back if she shows remorse and does the heavy lifting. Short of that, you are telling her that she can cheat you will do nothing to stop her. You will be in a one-way open marraige if you do not get angry and act now.