My first suggestion would be a .38 special revolver, . . . a Smith or Colt used police in 4 inch barrel configuration.
Revolvers for SD are like Kodak camera's: point and shoot, . . . and she's got 6 rounds to either change the perps mind on his persuasion, . . . or make him room temperature, . . . whichever happens first.
It is a proven fact that the vast majority of firearm altercations results in one or the other hightailing it, . . . and she could rely on the Kodak factor and the hightailing probability as factors that would keep her and the kids safe.
Her size and inabilty to train rules out the semi-auto and the rifle from the get go, . . . and I personally see a shotgun as a liability, . . . instead of an asset.
You have to either chamber a round when trouble comes, . . . or you are constantly loading, unloading, . . . making ready or making safe, . . . and sooner or later, . . . untrained hands WILL cause an ND just from the handling. Additionally, . . . the recoil is more than most women want to deal with, . . . and it's a whole lot easier to disarm anyone with a long gun than it is with a pistol.
The .38's are fairly plentiful, . . . I've seen them go in the easy $400 market, . . . sometimes less.
May God bless,
If you can breathe, . . . thank God!
If you can read, . . . thank a teacher!
If you are reading this in English, . . . thank a Veteran!