Her family should know. They are perhaps in the best position to exert influence on her, if, in fact, you feel they would be supportive of the marriage. Would they be??
My daughters and my wife's parents were more instrumental than anyone else in getting my wife to end her affair.
LIS, it sounds like doing this would represent a "180" for you from your comments. I don't recommend the "tough love" approach sometimes (or at least I would recommend some real qualifications to it) if your marital history was that you were too controlling, too stern, etc.
