(1) The father and mother of a minor child have equal rights to maintain an action for the expenses and the actual loss of service resulting from an injury to a minor child in the parents' service or living in the family except that where one (1) parent is dead or has deserted the family, the other parent shall have the sole right to maintain the action.
(2) In case the father and mother of the minor child are living apart and one (1) parent has exclusive legal custody of the child, the parent with legal custody has the sole right to maintain an action for the expenses and the actual loss of service resulting from an injury to the minor child, except that the noncustodial parent in such case shall have a right to maintain or join an action brought under this section, for the expenses resulting from an injury to the minor child to the extent the noncustodial parent has paid those expenses.