I would POLITELY inquire as to who had falsely accused me of carrying a firearm. Especially if you politely allowed them to see you were NOT carrying one. If they refuse to share that info, POLITELY ask to see the Administrator,, and ask the same question.
If it's a "known" thing that you often carry,, and the ASSUMED you were carrying,, then you can use it as a teaching moment to show the Administrator that you are a law abiding, polite gun owner. Show that you'd seen the sign, and had obeyed the law or regulation.
And then,, once you establish that you are not some crazy gun nut who's going to shoot up the place, you can ask a few polite questions.
Things like;
Since this facility is posted,, what are your security procedures to protect me, and my wife?
Who IS authorized to carry in that facility?
What insurance company do you use, so I know who to sue in case my wife or myself get injured by someone while we are here,, defenseless, because of your policy? Say it's a liability issue.
Questions like this often get the management folks upset,, because you actually politely question their authority,, AND put them into a position of being LIABLE for your and your wife's safety.
And when it comes from a well dressed, polite elderly gentleman,, it also throws them off guard,, and they are often, left without the ability to give you plausible answers.
However,, if you DO ask such questions & such,, it's possible that they may decide to remove your wife from the facility,, "due to security concerns."
In any event,, I'd have to at least let it be known that I'm a polite person,, who only wants to be treated with the respect due me. And to be unjustly accused is an insult to you. Plus,, by doing such inquiries in a calm, polite manner,, it shows them that not all folks who carry a gun are to be considered a threat,, but quite the opposite.
