olympus utough 800 ..12mpeg ,waterproof upto 10 m and shockproof takes brill pics has auto stitch and does video is around the 200quid mark
2nd'd
Also try taking your mum into a camera shop - a propper one not a supermarket. Spend 1/2 an hour going through the different models and fine one which your mum is confortable with, can understand the menu's... Any camera over about 7Mp is going to look as good as the next on a 6x4 photo, over A4 and the high Mp camera's come into their own.
If your looking for quality, go for a camera with the largest sensor as possible (that's physical size not Mp). More light, better picture.
If your mum is looking to get 'into' photography, then your just touching 2nd hand digital SLR prices at that. For rapid fire shots, a compact will never come close to an SLR - there's always that 1 - 2 second delay between pressing the button and the shutter going. SLR's can also take 3 - 7 shots per second.
Go to a shop though and have a word, they won't sell you the most expensive camera they can, they will probably give better advice than anyone on this forum unless they are a professional photographer.
just my 0.02