I think KyJim found a use for the Beretta 86. I've always wondered what the hell they were good for. Sounds perfect though, easy to load with the tip up barrel, manageable recoil, and she should be able to handle the weight. I like it.
The problem here is that even though the .380 isn't a barn burner, the guns are blowback actions. This means stiffer recoil springs to keep the slide locked during firing and more perceived recoil. A limp wrist will induce FTE's more often on these than a larger caliber gun. The problem is that seniors can have just enough arthritis that causes them to limp-wrist the gun. If not now, that can happen in the future with age. If considering a .380, rent her a Bersa .380 for testing which should be similar in effort of use. Food for thought.
What about a .22 magnum DA revolver. Smith makes a couple, as well as Taurus. Easy to use, easy to shoot, and low recoil.
The .22 Magnum is a formidable little cartridge. But I would not feel all that comfortable with it as a defensive round. The other downfall is that rimfire cartridges are notoriously less reliable than centerfire.
You might also run across the .32 H&R Magnum revolvers in the form of some S&W 431 and 432 airweights or the Ruger SP-101. The cartridge itself has a low recoil signature, even in the airweights. Ammo is more expensive and the .32 H&R doesn't have any significant self-defense stats but power is similar to a .38 Special. Tip: If opting for the S&W airweights, invest in grips that cover the backstrap. S&W put a single groove there that pinches!
S&W 432PD, .32 H&R Magnum, J-frame, six-shots.
The .327 Federal Magnum is relatively new. No SD track record, but the ballistics are most impressive. Built for a 3" barrel or longer (Ruger's SP-101 was the original platform) its power puts it on a par with many .357 rounds. But ammo will be much more expensive (new cartridge) and recoil could be an issue, even with a steel gun. Muzzle blast and nighttime flash will certainly be an issue.
The J-frame Model 36/60 with a 3-inch barrel loaded with 148gr wadcutters may be just the right combination, depending on how recoil sensitive Grandma is. The wadcutter, while having low power, is plenty lethal at short range (7 yards or less) and cuts a "clean" hole. Its lower recoil allows a faster follow-up shot too. They're low recoil, low flash and the noise is less obnoxious indoors than +P ammo too.