Depending on their ages, and considering your mom's possible range of motion limitations, you might want to consider looking at a 20 guage or a .410 shotgun for their HD weapon.
Grantedneither has the stopping power of a 12-guage, and both put fewer pellets downrange per shot. However, the lesser recoil and the lighter weight may be the difference between their being willing to use it and merely having a shotgun in the corner.
Also, given you mom's situation, you may want to look into having them do the paperwork for an AOW and shorten the stock for her. Standard-length stock can be very difficult to maneuver and use from a sitting position. A shorter stock makes the shotgun front-heavy, so that may need to be adjusted as well.
Having said that, I now have a vision of your mom with something like a lamb's leg shotgun in a scabbard slung down the back of her electric chair, knitting you a nice warm scarf or crocheting booties for her next grandkid.
PS - Is the joystick on the same side as your mom's shooting hand? If so, please talk her into getting it moved to the otherside of the chair. Otherwise, she is literally a sitting duck. Moving the joystick will give new meaning to "shoot and scoot."
* edited to add PS.