How about getting her a saddle with springs under it in order to pacify your father's worries?
I agree that short rides would benefit your mother's health and back overall. She probably doesn't really "need" a saddle with springs for short rides around the neighborhood, but it might be something that you could use to quiet your dad about in terms of being easy on your mom's back. Tell him it's a special saddle for people with back problems. Like a placebo.