Good advice above, but you cannot guarantee aircraft type (on BA or most other airlines) - changes can and do happen.

I would suggest, given your mother's mobility situation, that you either:
1) choose to fly in First - it is definitely more spacious and comfortable and very accessible. If this is a one off trip, then maybe splashing out the one time would really be worth it.
You get better food and drinks etc and it would be a treat for your mother.
2) Book the most convenient flights as soon as you are ready in Club World and pay for seat allocation (if you don't already have it by virtue of status).
If it's old Club World, choose a window/aisle pair of seats and allocate the aisle seat to your mother. The aisle seats are very accessible and easy to get in and out of. Sit yourself in the window seat adjacent to her and you will face each other during the fight and can have a nice interaction. If the flight changes to CW suites, choose seats to suit.

In either case, I'd recommend booking mobility assistance with BA if your mother can't walk very far with ease.

Hope that's helpful.