Hi Heidi, what you're going to get here are a lot of opinions, but since you asked:
I ride a bike because i need the exercise. I am 58 years old and 10 years ago i was having serious health and vitality issues due to a life of inactivity. I live in a very hilly town (seattle) and while i can escape some of the hills some of the time, i can't escape them all of the time. I used to push my bike up some hills too, but nowadays I just ride.
While I am not suggesting that your mother CAN or SHOULD learn to ride up and down those hills, that's what cycling was about for ME.
I see people on power assist bikes all the time, and while they are sharing the dangers of the road with me, there is a fundamental difference just like there is with motorcyclists. We understand each other, we face the same dangers, but that's it. So if your mother wants to ride an Ebike, let her.
why not?