Cohabitation is no longer illegal in NC. I’m not sure that it would have much affect on custody unless the child would be in danger from this other person.
After 10 years of primary custody, your ex would have to show cause as to why it would now be in the best interest of the child that he have primary custody.
If you have the “no overnights…” statement in your divorce or agreement, it may present a legal problem, but since he has already broken that and it has been 10 years I don’t really see that it would be an issue. As comingclean2 suggested, pursuing custody would be costly and his not exercising his visitations regularly would be a factor you would want to bring up in court. On top of all this, factor in the wishes of your daughter who, depending on age, may be old enough for her wishes to be heard.
It sounds to me as though he is trying to scare you into either giving custody without a fight or not “replacing” him as a father figure in your daughter’s life. Since he has not exercised his visitations I would say that he’s worried that you will be a “happy family” and that leaves him out of the circle…I honestly believe that he would not win. Though you mentioned problems with the visitations, maybe you could suggest to him to take the visitations he’s already entitled to and see where that takes the relationship between them before deciding that he wants to spend all the time and money in court. If it improves their relationship or his sense of responsibility…that can only be better for you.
As a last resort, you can suggest to him that if he wants to pursue this course of action, then child support will have to be modified. It will come to light then that there is past due child support owed to you. Especially, if there is something in your custody order about child support. I say as a last resort, because it may be that after some discussion it could be worked out between you instead of jumping to threats as he has done…