I actually stand by Americans here. Home is a place where you can be safe and relaxed. No-one is allowed to break-in, even when you are not there. And even more so, when you are actually at home, then by law (here) you are allowed to defend it. It is the bugger who actually gave up his rights by forcefully entering your home. And he might be armed so it is either you or him. I personally think that this is something where you don't run away. It might not be even possible, if living in a block of flats.
Criminals are not stopped by running away from them, or letting them get away. I don't even understand how we have ended up with that. Criminals don't think like that. For part of the criminals, it is only the show of force that will teach them, if even that. The current prison system is too forgiving, if you ask me. If they want to get their civil rights back, they have to earn them by hard work - to the point that the rest of the people can actually think the bugger has indeed regained his rights and his crimes are forgiven.
The integrity of the society depends on the people living in it. Criminal activities are something which cannot be tolerated at all. Not even if your friend or family member does that. If you let them get away with it, do you think they will stop it before someone corrects the situation?
By the way, I have never heard of someone actually mistaking family member to a criminal. But I have heard of 12-years-old boys using live ammunition with hunting rifles and shotguns when playing their own mock-up war games. The people of that generation cannot be described as merciful towards criminals, and took part in "citizen activites" much more often than people nowadays. For Americans, it would equal to Tar & Feathers. Type of angry mob justice, basically.
But regarding the situation where someone is actually pointing you with a gun, it is far too late for anything but to hope for the best and give up the wallet. There might be something what you could do afterwards. Like calling the police, for example.
I've been thinking about carrying concealed and carrying the gun visibly, I would go with carrying gun visibly (cannot carry gun here legally unless going to shooting range or hunting, but US is different in this matter). It works better as a deterrent. But this on the assumption you know when to use the gun and when not to. And how to carry the gun also.
It is true that preventative measures are important. I think you did the right thing when you told the police about that incident, Mars. Next time be faster and they might catch them red-handed. Close to home no-one should be afraid of being mugged.
Mika