Instead of embarking on a lengthy upgrade procedure through the XP service packs, now might be a good time to review the life cycle of the machine your mother has (in simple terms, think about buying a new PC).
Bear in mind that MS is ceasing support for XP in 2014. While this does not make XP machines immediately high-risk, it may increase their vulnerability.

As to the SP upgrade process, there is much talk on the specialised web sites in this field of slipstreaming. Perhaps one of our resident specialists could go through the pros and cons of this approach...