Case law would seem to hold otherwize..
Case law in the state of Montana my friend, allows me to wear a .45 strapped to my hip in full view, unconcealed into any business I choose to visit.
Now, the owner does have the right to ask me to leave, or to take it off before I come in. But he cannot dictate what is in my car whether I work there or not.
Case law is relative to where you live.
A person's car is their property, and unless that business owner wants to be charged with breaking and entering, they would have no other way of knowing whether or not that person has a weapon in their vehicle.
Ban all cars and get rid of your parking lot, or not. But you do not have the right, under any circumstances, to dictate what I carry in my vehicle.
Period.