Are you using DW's proprietary Library Items? Or is Library simply a folder name in your site?
Yes Nancy I'm using DW's proprietary Library items, they are .lbi files.
Anissa, you don't understand my problem. The Library correctly shows at the top of the webpage, my issue is that is was also showing up in the middle of the code as well.
I found a solution:
Here was my original code that I was having a problem with:
<li><a href="mouthpieces/shew.html">Bobby Shew</a></li>

Here is the solution:
<li><a href="/mouthpieces/shew.html">Bobby Shew</a></li>
You will have to look close to see the minor change of added a backslash before the word mouthpieces.
To me this is a problem with DW when using Library's.
When I create a hyperlink by pointing to the file I want to link to, DW automatically files in the proper path to the link. This path works just fine, however, when I use this same process in a Library (.lbi) file it doesn't work correctly. This is what got added to my pages assigned to my Library file:
<li><a href="../Library/mouthpieces/shew.html">Bobby Shew</a> </li>
I get a ../Library/ in front of my link which makes the link defective.
I had to type in the backslash for all of these links and everything work fine now.
DW programmers, you need to look at this, I've wasted a lot of time figuring this out on my own. This simple solution would be for the program to always put a backslash in front of all hyperlinks as a default as this would probably take care of this issue.