IANAL, YMMV, all the other caveats...
If by "Gun Free Zones" you are referring to Title 18 U.S.C Part 1 Chapter 44 Section 922(q) known as the Federal Gun Free School Zones Act of 1995, here's the relevant (in my opinion) part of the law, with emphasis added by me:
(A) It shall be unlawful for any individual knowingly to possess a firearm that has moved in or that otherwise affects interstate or foreign commerce at a place that the individual knows, or has reasonable cause to believe, is a school zone.
(B) Subparagraph (A) does not apply to the possession of a firearm—
........(i) on private property not part of school grounds;
........(ii) if the individual possessing the firearm is licensed to do so by the State in which the school zone is located or a political subdivision of the State, and the law of the State or political subdivision requires that, before an individual obtains such a license, the law enforcement authorities of the State or political subdivision verify that the individual is qualified under law to receive the license;
........(iii) that is—
................(I) not loaded; and
................(II) in a locked container, or a locked firearms rack that is on a motor vehicle;
........(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.
It looks like to me, that if you leave the gun in your car unloaded and locked in a container, then you are not in legal violation of the Federal law. Otherwise, the law seems to hinge on whether you
possess the firearm. If you leave it loaded, locked in a container or not, in your car and then walk across the street to the school, are you still in "possession" of it? If you are, but you have a CHL from the same state that the school is in, then you should be "legal." If you are not legally in possession of it, then it seems the law should not apply since it specifically mentions "possession" as a requirement.
The law cited above is a Federal Law. The Motorist Protection Act is a Texas state law. The only portion of Texas law that has an effect on the Federal one is the Federal law's own exception for CHLs issued by the state. IOW, IMHO, the MPA does not allow you to be within 1000' of a school with a loaded gun.
As noted previously, I am not a lawyer, these are just my thoughts from reading the law -- you have to decide for yourself.
Here's a link to the Federal law, 10 USC Section 922. You have to scroll down a bit to get to paragraph "(q)"
http://www.law.cornell.edu/uscode/18/922.html" onclick="window.open(this.href);return false;