What rights do we have, Mother of an unwed 16 yr old teen mother & baby's father?

We live in NW Arkansas. I am a mother to an unwed 16 yr old girl who is the mother of a 3 mo old baby girl. The father is around but is into drugs. I have tried to get her to understand that he needs to get help & that maybe she shouldn't have anything to do with him until he does get the help he needs, he is 17. I do not permit him in my house as I have other younger children. He thinks he can come into to my home & take her whenever he wants. Does he have any rights to this child?? He wants to take the baby to Georgia for Thanksgiving, without my daughter because she works & can't take off, but I am against this. What rights do we have as Grandparents??? Please Help!!! Any information would be appreciated.

((Oh Yes, he did sign the birth certificate, even after saying he didn't think he was the father.))

You state the father is "around"; does that mean he signed the birth certificate or paternity papers at the time of birth so that paternity is established?

You should probably allow him limited and supervised visitation with the child at your home only for the time being. If he wants more, he'll have to petition the court for visitation rights. They'll decide the amount and conditions of future visitation. Until he does that, I wouldn't allow him to take the child from your home.