If you have a network set up between your computer and your mom's computer, you could easily send the iTunes folder to your current computer. If you don't have a network set up, you could use some sort of portable memory drive, such as a USB drive or memory stick, where you would upload the music to and then download from. Those with less memory will obviously make the process slower and more complicated because the drive would take a lot of reloading to transfer all the 3000 songs.
If you have an iPod, maybe this will help:
http://docs.info.apple.com/article.html?artnum=300173
