You are woefully lacking in your knowledge of the law. A patron who enters a business that is open to the public is legally termed a "business invitee." That is, the proprietor has "invited" you to enter his business, but that "invitation" can be revoked for any reason whatsoever unless the law forbids specific discrimination, i.e., discrimination against the "protected classes" is not allowed. The right to bear arms is not a "protected class," so if a businessperson does not want anyone in his/her store to be carrying a firearm or other weapon, he has every right to exclude that person.
The 2nd Amendment, like all of the other amendments in the Bill of Rights, exists to prevent the *government* from treating its citizens unfairly. One cannot invoke the 2nd Amendment to force a private business owner to give up his property rights, e.g., the right to control who enters his establishment.
Well, you're mostly right on this.
Businesses open to the public are considered under most state laws as "semi-public" places. Many of your Constitutional rights extend into those locations, most specifically those preventing the owners from discriminating on the basis of race, religion, creed, gender, and disability. Those rights aren't absolutely, however, so Disneyland can erect signs requiring minimum rider height for some rides, and warnings against anyone with a cardiac condition from riding rides which may exacerbate the condition. It's even been held that if an obviously frail octegenarian wants to ride the "Thrill of Death" triple looping double-twisting roller coaster, the owners of that ride have a vested fiduciary interest in not allowing such an action.
Put simply, if a business owner tells you "no firearms," whether in signage or person, then I'd respect that and leave. Failure to do so in most states constitutes tresspass. If it's concealed, the waters are muddied and in some states it's still tresspass while in other states it's not.
In contrast, when you're on truly private property i.e. someone else's home or apartment, there are no "public use" issues. If they say "leave" you'd better get.
