Well, the obvious option would be to move out but I will begin with the assumption that you would have done that if given the opportunity.
I would suggest first going to http://www.lizmichael.com/ninemyth.htm
There you will find an article title d "Nine Myths of Gun Control" Have her read this or use it to address the concerns she has.
Also look at http://www.justfacts.com/guncontrol.asp
I don't know if you have already, but you should take your mother to the shooting range. I have taken a few anti-gun people and it had always opened there minds and help flush out all the bull-@#$% that they've been spoon fed by the statist.
Lastly, tell her I said that I am a Peace Officer and we that do this job want you to keep your pistol and use it to defend yourself and your family. I would feel much better going home at night knowing that a murderer or rapist, and not your mom, was chilling at the morgue after you or your mom put him down.
Tell you mom that weapons cannot be inherently evil, survival does not favor the wicked or righteous, only the prepared. When and if the day comes that some @#$%bag decides to attack your mom, we cops are not going to be there right away. She would do herself a great service to make her mind up that she and she alone is responsible for defending her own life.
If none of the above works then I agree with what poster below....