[dbehsman]

provide an example to demonstrate what you are asking.

When a private property owner opens up his or her property to the public (ex. to do business), does that private property owner then have the right to say that a person's Second Amendment rights are no longer valid in the person's car?

[circlecity]

"When a private property owner opens up his or her property to the public (ex. to do business), does that private property owner then have the right to say that a person's Second Amendment rights are no longer valid in the person's car?"

There is no second amendement right to posess firearms on another's private property if the property owner prohibits it. The constitution also provides for freedom of the press but that doesn't give someone the right to set up a newspaper business in my basement or parking lot.

[Melas]

When a private property owner opens up his or her property to the public (ex. to do business), does that private property owner then have the right to say that a person's Second Amendment rights are no longer valid in the person's car?

Since the property owner has the right to deny carrying a firearm under other normally legal conditions as well, I would have to say yes. Legally speaking, what makes the parking lot special?