to help her not become lazy and unfit
To my mind, this is a misconception. It will be up to your mum how much she uses the electric assistance. If you think of the e-element as her insurance policy, you could argue that it might encourage her to be bold and make trips that she otherwise wouldn't make.
FWIW - I have several years of experience of delivering inclusive cycling programmes and I'm confident that the likes of Wheels for Wellbeing and their kind would back up my assertion.
I do agree about the weight issue - perhaps look into options where the weight is carried as low as possible to minimise the top-heavy feel.
Re the smaller wheels - my experience is that a bike with smaller wheels can feel more unsteady if your balance is sub-optimal. I'd encourage you to trial a smaller wheeled bike before you give that option too much serious thought.
You've had loads of good advice/responses on here - it's great to see such a supportive response to keeping your mum on two wheels!