Shouldn't the non-custodial parent have first opportunity to care for the child during before and after-school hours?

Sounds good to me. Check your State law. All things being even, it seems reasonable that a judge would grant you the right to take care of your children over some stranger, or in lieu of paying "child care expenses." Oklahoma law provides that "If the court determines that it will not cause detriment to the child or will not cause undue hardship to either parent, in lieu of payment of child care expenses incurred during employment, employment search, or while the obligee is attending school or training, the obligor may provide care for the child during that time." 43 O.S. 118(E)(13)(e). Here, non-custodial parents even have priority over the custodial parent's spouse.