In Oklahoma, legal custody is an arrangement that primarily defines which parent or person gets to make what decisions for a minor child. Who spends what time with the child (visitation) is a separate matter.
Married Parents. When parents are married they have de facto joint custody, that is, neither has more authority in decision making than the other. Each parent can make any (otherwise legal) decision they want regarding the minor child; e.g. enroll him in this school as opposed to that school, etc.