You should apologize for anything you truly did wrong, regardless of:
a) how she will (or won't) react to your apology; and
b) whether or not she apologizes for any wrongs done to you, such as her affair.
Try to operate from a basis of "What is THE RIGHT THING TO DO in this situation? What is the thing that God Himself would have me do, if He were standing right in front of me?"
