The situation you posit is somewhat unique, although not entirely unusual.
Usually, the non-custodial parent pays the custodial parent his / her share of the child support obligation.
In the case which you present, where both parents are custodial parents, no payment should be required to the other parent, but the child support obligation remains and should be used by each parent
For the benefit of the child.
Leonard M. Weiner, Esq. Divorce Solutions