Shot guns looked appealing, except for the mobility/handling issues. For the situations where such a firearm would be deployed, dinking around with a shot gun is simply impractical for reasons others have already described.
A handgun has advantages of mobility, size, and simple handling in situations where you don't wanna have to go to a closet, rummage around for the shotgun, load it, and then deal with it in the dark. A handgun can be loaded and deployed very closeby but out of sight.
Disadvantages to a handgun? Depending on the power of the weapon, you (1) may harm someone in a different room, or even the next door neighbor (!), or (2) you may need to have more than usual aiming ability.
We fianlly settled on Taurus' Judge -- a revolver (simple, simple, simple) that shoots .410 shotgun shells. If you get the 3-inch cartridge model, it will hold 3- and 5-slug .410 shotgun shells, or buckshot, or birdshot, or 0.45 hollowpoint long-colt cartridges. That's a lot of variety!
A friend (teaches gun classes for concealed-carry licenses here in Texas) has two of these, and he loads several different shells in each revolver -- so the first shot is birdshot, the second a 5-slug 410 shell, the third a hollow-point .45 LC round.
Biggest problem for your question is cost; with the current hysteria,they're running around $450 to $500 at a gun show.
And, as othrs have said, if she alrady has a .38 why does she need anything else?
By the way, Winchester makes a nasty round for The Judge: a round for the 2.5 inch cartridge that shoots three plated disks AND 12 bb-shot; a larger round for the 3-inch cartridge that expels four plated disks AND 16 bb-shot. Neither is much fun to meet on the wrong end of a barrell (I've just heard this and seen paper-target shot patterns).
You are thinking clearly.
I recently saw an interview with a reformed burglar and he said, a loud barking dog kept him away every time from that house.
You can have a howitzer at home, but if the intruder surprises you in sleep, he has the upper hand.
Keep your gun loaded unless you have useless idiots running around. My .40 and .223 carbine are loaded and chambered. My little mosquito is also ready with .22 CCI mini-mags. The 370 takes care if i’m still groggy.
Little shi-thead bust my door or window he may get an entire buffet of fun.