There was a story here awhile back that gave the writer's personal experience of how he had always blamed his father for divorcing his mother. It was during the time he was posting on the board about his own M problems, that his father finally told him the truth about his mother's infidelity. All those years he had refused to have a R with his father, b/c he had not been told what really happened......and was left to believe whatever his mother told him. With his father choosing not to expose the truth, he lost the relationship with his son. That story was an eye opener for me.
You and your W should face them together and sit both sons down at the same time to give them the news. I am not in favor of lying. At the same time, I don't suggest dishing out all the dirty details. I would not say, "Your mother and I have decided", as if you are taking equal responsibility for the decision to divorce instead of her doing the right thing and end her affair. Your sons are old enough to be told that their mother has met someone else and she wants out of the M. The only thing you've really agreed upon was to grant her a divorce. However, don't be surprised when your W resists telling them the truth, b/c most WW's want to be seen as "justified" to their children and everyone else.
It's not your job to destroy the relationship between your sons and their mother. It is your job to be honest with them. You are not trying to get them to take sides. They are young men, and will not appreciate being told some generic explanation for why their parents are splitting up the family. I feel some things between a man and his W should remain private. However, when it comes to why they got a divorce, children as old as yours should know the truth behind the D (at least, the basics).
That's just MHO.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!
