Different TVs have differing 'sensitivities' (i.e. their ability to handle weak signals) so the fact your TV can get good reception doesn't necessarily mean that a different make or model will.
More importantly though, every TV aerial is only a 'rough match' to each of the frequencies it's required to receive. (In an ideal world you should have a separate aerial for every TV frequency, so that everyone's roofs would be covered in loads of aerials). Your mother's aerial is a poor match for the frequencies of the missing channels, so it's not producing a strong enough signal for her TV to work with on those channels.
Theoretically your mother should get her aerial (and the associated cable) replaced but, since she gets most channels OK, a simple signal booster should fix the problem. Asda and Tesco both sell them for under a tenner, but this more expensive one sold by Maplin provides greater amplification:
http://www.maplin.co....gle&u=223504&t=module
Chris