I would have to guess that a fair chunk of that private school fee is profit that is lining someone's pocket.

OP, one thing that's not clear is, do the children need a paid adult watching over them (i.e. tutor is also nanny while parent(s) work)? Or is there a parent available to look after them during the day? If the latter, you don't need paid tutors/nannies for all those hours. And some of the budget can pay for online or live courses, which you could still supplement with tutors.