Hi, and welcome to Apple Support Communities.
Which exact iBook model is it?
You can choose from this list:
http://www.everymac.com/systems/apple/ibook/index-ibook.html
Which version of the operating system is it running now? If it's really Mac OS X 10.4.10, it could be updated to 10.4.11.
How much RAM is installed? Maximizing the iBook's RAM can help.
What kind of optical drive does it have? (CD-ROM, CD-RW, DVD, Combo, or SuperDrive?)
Some tips for optimizing YouTube viewing on an iBook:
https://discussions.apple.com/thread/2436156
Also, I've found that Firefox sometimes works better than Safari for viewing YouTube videos.
Find the video you want to watch on YouTube. Then restart the computer. (This clears the RAM so that it is all available for watching the video.) Relaunch your browser, and select the video from the browser's history. Don't have any other applications running except your browser when you're attempting to watch YouTube videos.
Tell her good luck with it.