A.C.
First of all, dating (and marrying, and having children with) one's second cousin is legal in all 50 states. It is not incest. It is not really anything. At that point, the bloodlines are so far removed that most people wouldn't even recognize their second cousins on the street. In most states, marrying one's first cousin is illegal, but not in all. One's second cousin isn't even a consideration. The only thing sick that I see about their relationship is that he was still with you when it began.
Secondly, I would be very careful about telling your ex-boyfriend that he cannot have visitation with the kids because he took them around his new girlfriend. No court is going to insist on supervised visitation for that reason, even if he did break your heart by cheating with her. If you file for supervised visitation, you are going to have to prove that your ex cannot be trusted around the children alone, and if the girlfriend is the reason, you're going to have to prove that she does drugs and such IN FRONT OF THE KIDS. I think that, by denying him visitation, you've created a lot of trouble for no good reason, and it seems petty of you.
Having said that, unless his name is on the birth certificate of your first child, or unless he legally adopted your first child, he has no rights to that child at all. If he takes her and hides her, it is kidnapping. As for the child you share together, yes, legally right now he can take that child, and although you could go to court for a custody hearing at that time, in many states, he could keep the child with him until the hearing. So get to a court and get a custody order in! Even if it isn't supervised visitation but just regular visitation, it will get the courts involved in your custody, and then if he takes the child, he will be breaking the law and can be charged with kidnapping. I would petition for a custody hearing at the same time that you file for child support. I hope that both of you can stop the finger-pointing and threats and eventually have a cordial relationship for the sake of your children. Good luck.