I know how you feel but would offer slightly different advice. Do invest in a good alarm system and also a large dog breed if it can fit into your lifestyle.
Handguns are great for concealed carry but, as stated, the shotgun is the best home defense weapon. However, no weapon is effective if you are not comfortable with it or are scared of the recoil. For that reason I would opt for a 20ga in a semi-auto configuration. The 20ga is nearly as effective in across the room situations as the 12ga but with much less recoil on the shooter. The semi auto action also absorbes some of the recoil by it's very nature. Further, a short barrel is desirable as it makes handling the weapon much easier in tight spaces. Finally, conside a "youth" model as the proportions are all going to work in your favor in a home defense situation as well as fit a smaller adult better. There are other reasons to pick the 20ga that have to do with the legal s***storm that will follow having to use a weapon in self defense

but that is a topic for another discussion and a minor consideration.
Here is a clip from a great article I read a while back:
"Remington 11-87 Sportsman Youth – As a compact, easy shooting shotgun, it is tough to beat the Remington 11-87 Youth. A semi-auto chambered in 20 gauge, this shotgun has a 21” barrel and a adjustable pull of length, meaning you can fit the firearm perfectly for the shooter. MSRP $804."
This, or something similar, would be my suggestion. Finally, once you make your choice you must get her to shoot it until she is comfortable with the system. Hope that helps