how about negotiating with the younger sibling and giving it a try ... say ... 3months or 6 months ... chances are that this child WILL find friends quickly and like the new school but if not ... you can return to the old school ... less convenient to have two kids in different schools but they won’t kick out the older child out of the private one once they are both accepted and with the money saved you can arrange after school care or transport if needed.
Unfortunately, some of the private/independent/parochial school contracts require full payment even if the child no longer attends. Read and understand your contract.
