If your mom is willing to carry a pistol, then she will clearly be willing to carry some small electronic devices. Seems that there are neighbors. How about a combination of things aimed at deterrent activities....something that would get the person to leave the area ...things like..
A cell phone, maybe the prepaid kind, that has every button set to dial 911. All she has to do is hit one button then proceed to explain the problem if she's able. If not, then responders are required to come to the house, even if the phone is hung up.
A remote that will activate LOUD alarms within the house and OUTSIDE the house... once set off, a particular sequence or process must be completed before they go quiet.
An automatic phone dialer...I have one for my dad...he presses one button on a locket around his neck and it transmits an alert code to a receiver which dials, in order until a human answers, 4 different numbers.... these should NOT be 911, but rather neighbors, yourself, relative who is familar with the situation and, hopefully, can respond from the immediate area. This can be good for many purposes, including "help, I've fallen and can't get up." Radio Shack and X10 sell a bunch of units that, with some study and ingenuity, can make phone calls, turn lights on or off, be activated by motion detectors or push button locket, etc.... very versatile but needs to be designed with the user, your mom, in mind.
Net....if she's not good with guns already, some few lessons won't really fix the problem...and you are facing advancing age with frailties over time.... best address the long term problem using technology to alert others to the fact that your mom has a concern, regardless of what its form may be.