Ok let me break it down for you in doses you may or may not be able to comprehend.
The situation is your think that owning a gun makes you MORE safe in case of a home invasion/robbery
First lets look at the robbers/invaders - they must have an agenda, so lets break that down first
1) They are there to rob you blind
2) They are there to kill you
Only two options unless they wanna put gifts under your christmas tree and drink a little of your milk - but that is not really a far fetched option as you already subscribe to the dumbest notions out there.
So lets deal with #1 first. They are there to rob you.
The ONLY way this will end up with a death is if you introduce guns/vigilantism into the situation - or you would HAVE to subscribe to the idea that they would kill you just for the heck of it (in which case we end up in bad guy agenda #2 again, and we will return to this)
So by you introducing a gun to the equation you have now put your whole family at risk - well done! (robbers usually do not think its a cool idea to add their own execution to any potential conviction)
Situation #2 - they/he/she are/is there to kill you.
If that is the case - there ain't **** you can do about it! You just caught some real real real real real real real real real real real bad luck and got a visit from your friendly neighbourhood torture master/insane murderer.
What you got on your hands is a mild case of paranoia - I am thinking more than likely Hollywood induced as this seems to be where you get your thinking.
Any way you put it - if you add your own gun to the equation you are putting your family at risk - they very foundation of your argument, and you are doing the DIRECT opposite.