If she has a relationship that you are uncomfortable with and she won't stop it, that should tell you all you need to know. You and your family aren't as important as her "friend".
This is a GREAT point, IDU. On Day 2 of discovering my wife's affair, when she was giving me the "he's just a friend" b.s. (and most of my intel hadn't kicked in yet, so I was hesitant to TOTALLY blast her as lying to me), I simply said to her:
"Even if that IS true, then what you're telling me is that you're willing to place your friendship with another man ahead of your husband. I can't live in a marriage like that. This is a dealbreaker for me."