Can a mother who is separated from her husband move her child out of state without father's consent?

A parent that takes a child out of the state with the intention of keeping them from the other parent could subject themselves to the risk of losing custody. If you leave and your husband files for divorce here a court could grant him custody and compel you to return. Under the UCCJEA (Uniform Child Custody Enforcement Act) the state in which a child resided six months prior to the cause of action has jurisdiction over the child. I would retain an attorney here then file for divorce and custody also seeking permission to relocate to your home state citing family ties etc.