The parents are not married have a child together living with father of the child's parents and both mom and dad want to move to another state, can the grandparents stop us and take the child?

How old are the parents?

Assuming that you are both adults and not minor children who have a child. No,

If they would stop the legal parent who has custody of the child, you would merely call the police

If now the mother is 14 and living at home with the child, it can depend on state law.