Qualifying for Elite on Jan 4? 35,000 miles in <4 days must be some sort of record! Anyhow, my guess is that it's a 2010 Elite package only and not 2009+2010 Elite right? Someone correct me if I'm wrong, but unfortunately, the Elite status actually doesn't start until March 1st for those qualifying right at year's end. The package probably won't arrive until mid Feb at the earliest (Mid Jan for the next sweep of new Elite packages to be sent + 2-3 weeks mail time).

It might start showing up on your boarding pass with a *G for UA flights in mid Feb but if your mom is flying out at the end of January, chances are, she won't be getting the Elite perks officially yet.