I bought my daughter a 410 for self defense last year. I tried her with a 20, but she literally dropped the gun on the ground and would not touch it after one shot.
I bought a 410, and some short bird shot, and finally got her to shoot it. Then I made her cycle three boxes through it at 15'. Then I reloaded it with 3 1/2 self defense rounds. She has not shot one of these yet, and hopefully won't have to.
It really depends on your wife. My eldest daughter, (same size as the younger), will shoot anything I will and never flinch.
Ben