Which airport are you coming into, TSQ? Might make a difference for how far you want to travel for a hotel and that. Have you 'done' London before?
I always think the museums are London's best feature. Most of them are free, and the collections are amazing. Some of them have a slightly increased likelihood of "exuberant" children during the holidays (especially the Science Museum and the Natural History Museum). The Victoria & Albert, the National Portrait Gallery, the Tate and the British Museum are free, fascinating, fairly relaxed, and have lots of seating throughout so you can take a rest between looking at exhibits.
By contrast, there are some of the Big Attractions in London which are ridiculously expensive. The Tower of London, the London Dungeons, and Madame Tussauds are really expensive, and tend to have massive queues, and are a bit rubbish for people who need to take things at a slower pace. I'd personally be inclined to steer clear of them.
There's also the London Eye - it is an amazing view of the city if you go on a clear day, but really expensive. When I have friends over I'm inclined to take them on the river cruise instead - still a great view, sitting rather than standing, good audio commentary of what you're seeing, and much cheaper.
How is your mother's mobility post-operation? Because the cheapest/easiest way to get around to see things in London is with a day-pass for the tube, but some stations do require a fair bit of running around in underground rabbit warrens to get from platform to platform. It might be easier to pick one area - like South Kensington, or the South Bank - with two or three things to do which are close together and do that each day. How long are you staying?
