First remember that having a great marriage or a bad one does not cause an A....that was his choice. My WW is still in the stage of blaming others and justifying her actions on the slightest imperfections she saw in our marriage. She even changes history to suit her (revisionist). So we have a long way to go.
I also have 3 GREAT kids similar in age. That is one of the reasons I have decided to attempt to R (that and I feel it is worth the attempt)
However, the kids knowing does complicate thins. Mine know nothing of the 6 year A with someone they know and trusted. They were even Facebook friends with the OM.
Next read 180 note in FAQ section. I wish I would have known this (lucially I did it out of instinct somehow).
This has been to my great advantage. She has never seen me get upset or raise my voice even when I called the OM to reinforce her breaking all contact with him.
Remember to take your time...there is no hurry for anything unless someone is in harms way. Then you can take the time to get past the shock and decide what to do on YOUR terms.