20 gauge is absolutely the wrong choice. 20's are lighter and ammo makers try to pack the same punch as a 12 gauge into their offerings.
Even with lighter loads, the 20 is still a light weight gun and recoils more. Additionally, the circumference of 20 gauge rounds and chambers makes loading them on the clock more difficult.
A good 12 gauge with Winchester Low Noise - Low Recoil (a.k.a. Featherlite) or Federal Metro loads will be the softest shooting shotgun you can have with factory loads. Here's a place where handloading comes in real handy. You can make your own rounds that will perform as consistently as Featherlites with even less recoil than those rounds deliver.
The stock length is very important to the amount of felt recoil. And, mounting the gun properly to the face is extra important.
I have one observation about recoil sensitivity that seems important to share. The amount of noise a gun makes seems to have an affect on the psychological perception of recoil. Make every effort to get sub-sonic loads and use them exclusively. Metros and Featherlites are sub-sonic. If you give her 2 3/4 dram ammo (or hotter), she will not be a happy camper. Longer barrels are quieter as the combustion is more complete before gas leaves the barrel.