Sorry to read about your families challenges, I hope all your challenges get better.
I am going to recommend a few things not all "type of pistol" related.
Sign her up to take a Women On Target so she can get some great hands on training in a safe, comfortable environment.
Secure the house, outside night lights, better door and window locks. Remember you have had a break in, so they now know how to get in.
Make sure your mother handles many different pistols and fires them. What we think is best (as men) isnt always the best for others. Take her to a range with rentals or if you are near a C3 monthly shoot take her to one and make sure you announce that you are coming and why, Calgunners will bring out to armory for her to try.
Once she has chosen her firearm make sure she goes to the shop and buys it and buys the cleaning kit and cleans it and takes a class or two.
Just some thoughts.
Here to help
Jacob Rascon, (aka) Pennys Dad
CALGUNS Shooting Sports Association.
1. Blessed be the LORD my Rock, Who trains my hands for war, And my fingers for battle 2. My loving-kindness and my fortress, My high tower and my deliverer, My shield and the One in whom I take refuge, Who subdues my people under me.