Hi Micro! How's Italy? Posting in the "using moodle" section to get answers on using Moodle itself but his really isn't a Moodle question as much as a structure question. So, let me take a break with you on this!
It's not much different than any other access to a data structure with assigned restricted access. The question is...why would you want to break it up into different schools? When you register students you assign what classes they are in. So, I'd just structure your classes by type. For example, if math, all geometry together and so forth. Then you just assign each student to their math class. I wouldn't make it to complicated. I'd make all the teachers part of your one "moodle school". The students can only see the classes they are assigned to anyway.
The teachers can only access their classes as well. Only people way up the Moodle administrative chain would even see a difference. If they wanted a split structure they should have a different moodle for each school.
Such a beautiful area of Italy your profile has you in!