Can a child that lives wit the mother that have joint custy of the child can he move to another state with the father?

Answer 1

That depends on the state where the custody order was issued and the order's provisions, but in general, joint custody implies that both parents have equal say in decisions affecting a child's life and either parent has the power to ok or deny a decision such as a move, especially a move that would prevent a hardship to another parent in terms of their parenting time with their child. In other states, any child under a custody order is under the custody of the state as well, so any proposed move not only must be ok with both parents, it also requires permission of the court.

When in doubt, refer to the custody order, or at least provide the legal state (or country if outside the USA) of the child's current legal residence.