OP, in your original post you say that it is YOUR choice to host the share
"We host the nanny share, and this is our preference."
But later you try to make the case that you hosting the share is for the OTHER family's benefit
"In the other family one of the parents works from home so this is why we don’t rotate houses and why often it’s not a huge rush or inconvenience to get the kid here...given that the other family uses their house as an office, they benefit in many ways from us hosting."
Which is it?