The items I have purchased in the itunes store are not showing up in my libray. A few are on my actual ipod touch, but not in the itunes library. Is there an easy fix to this or is it maybe something in the settings that I'm missing?

It's just not making sense to me that it's a purchased item from the itunes store and it isn't appearing in their program.

She can choose to either enable the setting on her iPod to Manually manage music and videos.  With setting enabled she can sync content to her iPod from multiple computers without it affecting whats already stored her iPod. For more information on syncing content to an iPod manually see this article. 
http://support.apple.com/kb/ht1535
However, I would recommend copying whats on her iPod to her iTunes library first.  There are several ways to accomplish this.  See this older post from another forum member Zevoneer discussing the different ways to do it.
https://discussions.apple.com/thread/2452022?start=0&tstart=0
B-rock

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