Greetings to you and your mum. I've got a grandma who loves to fly, luckily she remains fully mobile, and prefers solo travel, I think I must cramp her style. Anyway welcome TCM1976JJC, welcome to Flyertalk and in particular to the British Airways board, and I hope you and mum will continue to post here. So let us know how it goes.

Personally, in your shoes, I would book a day room at the Sofitel in T5, it is connected to T5 internally with step free access and I believe the wheelchair assistants are willing to go over there. She can then have a quiet rest and use of the bathroom, while may be you go over to the Arrivals lounge for a bit, there's a Concorde Breakfast room there. Then about 2.5 (or so) hours before departure think about heading over to T3 via the Heathrow Express. Again it's step free all the way. You should get an hour in the T3 First Lounge there, there are some views in the dining area but also a lot of scaffolding!