No couort order for either mom or dad to have custody

My grandson left his child with mother in Mo. and moved back to
Al. They were not married. He is now paying child support and wants to see the child. (17 months) Mom says only if she brings child to Al., or he comes to Mo. Paternity is not a question. Can my grandson be arrested for kidnapping is he comes to mo and takes the child to Al? What would be steps to take to gain custody if he took him to Al? Again, there has been no court ordered custody granted to either mom or dad. My grandson lives with a woman in Al, and the mother of his child is adamant that child cannot be in her company. Yet she can leave the child with her mom while she works, and her mom has a long history of drug abuse, and at present does not even have her own children as they were removed from the home and have not beeen returned to her as of this date. Mom is very jealous of other woman. But the main thing I want to know is can my grandson be arrested for kidnapping if he takes the child and goes to Al. with him?