Yes.
North Carolina can be quite strict about this, and Mom can easily have a "no paramour" clause written into any separation or custody/visitation agreement. This doesn't mean that you cannot see your daughter, but rather, you cannot bring any love interest around your child during your parenting time.
Provided your intended paramour is not the cause of the separation, you should be protected from an "Alienation of Affection" suit.
Tread carefully. And think about your daughter too - it's generally not going to be in her best interest for either of her parents to be dating while still married.