What happens if both parents agree about the custody and visitation but there has been a history of domestic violence?

If both parents agree as to a parenting plan as it involves the custody and visitation between each parent and any minor children, there's a good chance that a court is going to approve it. However, a court does have the responsibility of determining the best interest of the minor children. The court can override that agreement if the judge feels that the agreement is putting the children in the threat of harm some way, and they can make it so that there's less time sharing or supervised time sharing by the violent party.