What you might want to remind your mother of is this one simple fact. In the late 80's, and early 90's Washington DC had the HIGHEST murder rate of any city in this country per 100,000 people. This was going on in a city that at that time had BANNED ALL handguns and all rifles and shotguns had be kept unloaded and locked up by law.
The simple truth of the matter is this. Criminals DO NOT care what laws are passed. They are criminals, they break the law. They will get guns anywhere they can and then use them against an unarmed victim because it's the path of least resistance for them.
Now take a look at the state of Florida. They also had very high violent crime rates in the 80's and early 90's. Then they decided to start issuing conceled carry permits to anyone who wanted one. They relaxed their gun laws and the average citizens started to arm themselves. More guns were on the streets and in the homes yet the violent crime rates decreased significantly in a few short years. During those years after they became a shall issue state, there was an increase in private citizens defending themselves against attacks, but they were not prosecuted for doing so. Now the criminals don't know who is armed or not. Crime has gone down because crooks being crooks, don't want to take on an armed person who just might shoot back, or shoot first.
A firearm, be it a handgun, rifle, or shotgun, in the hands of a law abiding citizen is no threat to anyone except the criminal that makes the mistake of trying to do something illegal to that law abiding citizens home, family, or person.
Personally I've pulled a gun twice on people. Both times MY property was being violated by criminals. My guns and I stopped them. No shots fired thankfully, but I kept my property and they went to jail and the police told me good job and to have a nice evening when they left.
My mom like yours worked in a hospital ER. My mom also worked in surgery, so I understand her point of view and the perspective she has regarding guns. My mom tends to feel the same way. However I think for her to say handguns are the reason for people being shot and if they were all gotten rid of is a bit nieve. Evil people will do evil things no matter what. The laws just don't apply to them until it's too late, and at that point how does a person justify to the victim that it was in their best interest to take away a tool that could have been used to protect themselves?
I'll never try and tell someone they have to own a gun, but there are alot of people out there that would love to take mine away, and the only reason they have for wanting to do so is fear of something that in my hands is alot less dangerous than the car they drive to work every day. It's irrational and without any logic. People that fear guns are for the most part completely ignorant when it comes to guns. Yet they would deny me my right to own something I am totaly comfortable having in my home or carrying on my person because they are afraid of it.
Just my 2 cents for what it's worth.