To answer your original question, NO you do not tell her family, etc. Have you read DB or DR? If so, they do a much better job of explaining why in detail but the short version is that this is NOT about pressuring her into doing what you want. It's not about you forcing her back into a marriage that OBVIOUSLY wasn't working for her in the first place. It also isn't about who or whatever she's doing.
It's about looking at the REAL issues of your marriage and since you don't really have much of one right now, that leaves you looking at YOUR part of the marriage and it's problems.
Focusing on her and trying to "expose" her "dirty, evil behavior" may make you feel better but is not really likely to bring your marriage full-circle and on the path to reconciliation.
Again, this is not about all the "extra" stuff going on, it's about what isn't going on with you. She can be forced to quit that and then work on what she doesn't want to work on. You also can't force her to stop "walking away" and then expect her to believe things you change are "for real".
Start today making changes in YOUR life. BE the man you want to be and let her see that you're serious about changing FOR YOU!
I check back, but the bottom line is that this site, these books do not advocate, in ANY way, exposing the affair.
Affairs may indeed flourish in secrecy, but if you know, it's not a secret anymore now is it?