You can probably achieve a lot even if you select just one afternoon in a week. And you should try to optimize also for fun... maybe it will be the kids' favorite afternoon in the week. For example, you could offer your neighbors who have children in the same age, to include them in your "afternoon school"; then the children will get each others' company as a bonus: it's more fun doing things together with friends.

Also, you can start before the school begins.

Yeah, it's not the same as being allowed to optimize freely, but you can still try to optimize within given limits.