Hi Bob - I have a Hayter electric start rotary mower (key operated) and it's supposed to be semi-self propelled - whatever that means - but I wouldn't recommend it for a sloping lawn. I've enough problems getting it deal with uneven - though relatively level - ground. I wish I'd tried it out for myself before deciding to get it. I only had a demo by the salesman, which I now realise was a mistake. The problems I find are firstly that the charger unit is very difficult to plug in and also to unplug, and secondly the grassbox is awkward to empty - something I only discovered for myself having used it.
So, I'd suggest that you get your mum to actually try a mower herself, in spite of what a salesman might say about its performance and ease of use. Good luck!