The applicable law is very clear. 948.605:
Specifically 948.605(2)(a)Any individual who knowingly possesses a firearm at a place that the individual knows, or has reasonable cause to believe, is in or on the grounds of a school is guilty of a Class I felony. Any individual who knowingly possesses a firearm at a place that the individual knows, or has reasonable cause to believe, is within 1,000 feet of the grounds of a school is subject to a Class B forfeiture.
948.605(2)(b) give exceptions. The only exception that would apply to a CCL holder normally, whether in a vehicle or not), is 948.605(2)(b)1r Except if the person is in or on the grounds of a school, a licensee, as defined in s. 175.60 (1) (d), or an out-of-state licensee, as defined in s. 175.60 (1) (g).
If the car is on the grounds, the person is on the grounds.
So... if you want to have a firearm on school grounds, it needs to be according to 948.605(2)(b)1m A person who possesses the firearm in accordance with 18 USC 922 (q) (2) (B) (i), (iv), (v), (vi), or (vii).
which points to Federal Law which says:
So.... as you can see, you have to follow a trail but the trail shows that having a loaded firearm on school property is usually a felony.(B) Subparagraph (A) does not apply to the
possession of a firearm—
(i) on private property not part of school
(iv) by an individual for use in a program approved
by a school in the school zone;
(v) by an individual in accordance with a
contract entered into between a school in the
school zone and the individual or an employer
of the individual;
(vi) by a law enforcement officer acting in
his or her official capacity; or
(vii) that is unloaded and is possessed by an
individual while traversing school premises for
the purpose of gaining access to public or private
lands open to hunting, if the entry on
school premises is authorized by school authorities.