I think you are in between a rock and a hard place. Pressing your employer will only make you the sore thumb. There is another thread about this and I copied the reply that apostate gave, it is in red:
Here's how I read it:
If someone doesn't have a CHL, the refinery [1] can prohibit them from having a firearm in their vehicle anywhere on the property.
If an employee does have a CHL, the refinery can prohibit them from having a firearm in special parking [2] but not in other parking areas.
[1] For example. More generally, "property owned or leased by a chemical manufacturer or oil and gas refiner with an air authorization under Chapter 382, Health and Safety Code, and on which the primary business conducted is the manufacture, use, storage, or transportation of hazardous, combustible, or explosive materials"
[2] special parking = "parking lot, parking garage, or other parking area the employer provides for employees" within "a secured and restricted area:
(i) that contains the physical plant;
(ii) that is not open to the public; and
(iii) the ingress into which is constantly monitored by security personnel."