He doesn't have that right as long as they are using their cars to advertise for a political party OFF his property. Just like she does not have the right to use his property to advertise for the politician of her choice.
By your reasoning, a Catholic Church would have no right to tell an employee that they could not have a pro-choice bumber sticker displayed on their car on church property.
You speak like she hung a banner across the front of his business. You speak as if she's a simple guest. She is an employee like all the others and has been discriminated against, because of the particular message on her property. The employer's property is irrelevant, because all the others are allowed to park their property in his lot w/o comment. Additionally he was involved in electioneer on company property and welcomed other bumper stickers.
The facts are clear. He intimidated the woman to silence and abandon her first amend right by threatening job loss. He violated 18USC245.
The church should be more discrete in their hiring. Now this scenario is as if the church was Pepsi and the employee brandished coke products. Or, the employer was the RNC and the employee was a Kerry supporter. The context makes it entirely different. The woman's sticker was not related to her job. It was related solely to her political choice.