While I understand the LEO hate these type of situations, since they can often turn ugly. You could legally have a handgun in your vehicle, without a LTC. Since you were not lawfully detained, or stopped for a traffic violation, you are not legally required to show your LTC, whether carrying or not. (Why you don’t carry 24/7 is your call)
I can only surmise that there is a past, non positive, history with LEO, in your area, or as a result of your son’s dealings with his marital situation. I am always ready to fully ID myself to LEO, including my LTC, for two reasons: They will know, that I am not a threat to them, and that if things go south, I will be the one viewed as the most cooperative.
I understand that I have 1st, 2nd, 4th, and 5th amendment rights, when dealing with law enforcement, I also know that trying to defend those rights on the street, can often be counterproductive. JMHO