On an aside, many modern new school are designed so their car parks don;t have enough parking spaces for even the school staff, its a council thing to get more people to car share, or use public transport.
As to parking for students at a school, well, how did they get to school before they grew up enough to get a driving license? By foot, bike, bus? Go back to it!
Teaching staff in schools, of which I am one, carry a lot of stuff home at night, often a laptop computer, plus books, plus papers, plus subject specific stuff. Me thinks they should get priority over children! Lets be fair, most secondary schools take kids from a maximum of 1.5 miles in large cities, 2 miles in smaller cities, and 4 miles in the 'burbs. Only time that students 'need' a car is if they are having to travel out of their local school zone for specialist teaching (e.g. local school doesn't offer the subject/course the student requests) or they live out in the sticks and travel miles to school. In such circumstances, local authorities cover all, or the majority, of travel costs.