A revised version of this plan would possibly be to have a rotation of volunteers in each shul, such as if a person has an emergency (hopefully a good one) to call on certain people such as the A family available 6-10 on monday and tuesday, the B family available on sunday afternoons… I know of a shul that has a similar program in place. They set up a rotation for meals for someone who had a baby etc and it’s beautiful. But getting back to my idea, in this way, people would know who they’re leaving their children with and wont have to worry.
Problems will come up when the rabbis daughter gets married…