keep in mind, her type of activities are not what a "role model" parent, and you have a VERY strong case for custody, trust me. Also, in the custody agreement, you can have it say that no "unrespectable individuals (insert other guys name) may be around the children ever." it will hold, and if she violates this rule, in any way, any bit of her custody will be revoked. Adultery is not good in the courts, and certainly not the kind of behaviour that a parent should be exhibiting, but it does happen.
If you go that route, gather evidence, make sure you yourself are clean, and go for the throat in court, You'll basically get a restraining order so that her new friend will not be allowed around your kids, joint custody, hence ruining any permanent chances of her and his relationship