I teach CHL classes in Tx. As a teacher in Tx, I have also come up against this issue personally. I can understand the confusion but your wife can not have a firearm in her vehicle (education code trumps labor code in this case) UNLESS she has permission from administration. She should carefully check the teacher handbook for her district to make sure she didn't agree to the no firearm on school property rule. Signing her agreement in the handbook can be considered effective notice to not carry.
I solved this by parking just off school property.
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