Ah yes, Young Alexander Purcell. Kirby Ross and I worked hard on Capt Purcell and his Scouts over a period of years. Best thread to describe family is here:
http://history-sites.com/cgi-bin/bbs62x/mocwmb/webbbs_config.pl?page=1;md=read;id=23713

Your family lore about the gun belonging to his son George rings true with what we know about YA. The issue you have is provable provenance which is what you are really asking for. I can't provide that, but the history of YA Purcell whereabouts and actions during the war are documented on this board as accurately as you will find. Guerrilla bands such as his picked up and lost firearms at an amazing rate. Frequently in these hard riding cavalry units, the individual would have multiple firearms, 4 handguns were typical, six not unheard of. To prove you have a handgun that YA Purcell carried during the war may be very difficult lacking first person affidavits that accompanied the weapon. Even old receipts, daily journal entries showing it was received in payment, etc would work. Does it reduce its market value not having such provenance, yes. It will be typical antique civil war era antique gun price. Does it reduce the family legacy value? Of course not. Look how much you have learned about one of the shadowy, least documented unit and leader of the war in Missouri. Document that history for your children, they won't find it with AI or Google.

Kirby Ross still lurks and is really the expert on Purcell. I defer to him for the definitive unit history. Sadly the age of the board is starting to show as we have lost many of the excellent researchers that have contributed over the last 20 years due to age and illness. I hope we can keep it going as it is a repository of amazing work of historical importance.