CCW is prohibited on public k-12 schools but they are allowed in your vehicle. you have to take an extra step and make sure it is in a compartment in your car, as well as the vehicle has to be locked.

I would think that would apply to the school. they can't control your personal property. now if you are in dorms, they can control that even though you rent it, but if the car is yours you have every right to keep whatever you like in there as long as you are legal to own it.