I have serveral comments for you:
1)Price: The R series are often cheaper than the T series because they are a bit thicker. The T series is the premium thin version and at a certain point, thinner costs more. The R series uses the same motherboards and is basically (excepting graphics in certain cases) as good inside for comparable models.
2) Quality: The R52 came out a little later than the T42 and is more similar in advantages and issues to the T43.
The T42 is a bit older. Quality is the same, performance may be a bit better with the R52
Your mother will probably never know the difference unless you go to upgrade the hard drive. The R52 or T43 are pickier about which hard drives, than the R51 or T40,41,42.
I understand that the R52 or T43 is least likely of all it's siblings to have motherboard problems. R50, R51 and the T42 are next most reliable
Although many people never have any problem, the T40 or T41 are considered most susceptible to this known issue, and I personally don't recommend or buy them.
3) Seller: I'd investigate USA notebooks before buying from them. Check their reputation. Having a nice website does not mean they are particularly trustworthy or any less risk than ebay, which is definitely cheaper. I do buy on Ebay, but buying on Marketplace here has been a very good experience for me and you will usually find a better condition machine and get more personal attention from sellers here like Harryc, Ajkula66, BobA and many others. These guys care about the stuff they sell and are not just pumping product through. There are sometimes better deals than Ebay but you always get solid value for the price here and I think it's the lowest risk way to buy used.
4) LCD. If your mom is not carrying it around much, then she will probably like the 15" better. There are different resolutions availible, and you may want to look at XGA or SXGA+ and possibly UXGA screens to see which she would prefer. XGA is cheaper and most common, though.
5) Alternatives. For an all around good machine for incredible value, the R51 is worth considering. A 15" R51 will go for around $300 on Ebay nowdays. There are about 40 R51s for sale at any given time. Competition is good!
Not recommending sellers or even Ebay, but look at these to get an idea of price and realize that you are buying the same off-lease machines from USA notebooks.
15" R51:
http://tinyurl.com/664g4q
15: R51 that a friend is bidding on:
http://tinyurl.com/5tksjp
15" R51 with SXGA+ screen:
http://tinyurl.com/6zljak
here's a 14":
http://tinyurl.com/6fqkl6
If you do choose to buy on ebay, you can always post a link here before bidding and see if anybody sees a shortcoming...