As long as you are in lawful possession, I have no right to bar you from the curtilage of my property. I can under the castle doctrine, prevent you from entering my domicile.
But folks lets leave aside the business aspect and private property for one moment. Can the government especially local government prevent me as a teacher from having a gun locked in my car? Because once I roll off school property....I'm in da HOOD......
Must you provide justification for keeping a car off your property? IMO, it's the property owner's discretion, no justification required.
But yeah, leaving aside the property rights issue, seems to me that in some schools the teachers ought to be armed in the classroom.