It’s worth seeing if you can’t get a higher res display. More res is always better. I know they have 15" displays that will do 1920x1200 which might be overkill for your mom and her email, but for icon intensive apps its awesome.
The vid card should be fine, and the processor is OK but it’s one of the lowest end core Duo’s by todays standards.
With those specs I wonder why not just get a Dell? Alienwares tend to have a premium and if you aren’t getting one of their ridiculously spec’ed machines you might be able to save a lot of money on the same computer.
Check out www.gotapex.com for good deals on Dell laptops (updated daily)
With Alienware and even mac you are paying alot of money for the brand name. For example i built my pc for 1000pounds, the same spec Alien ware PC at the time when i was looking was at least £600 more expensive