To change the location of the library (only the database files):
File > Library Manager > Add...
Name: [can be anything]
Location: a folder on your flash drive
Clone: select the source library
To fix the base folder path (or paths if you have many -- fix each path separately):
Select all files and use the "Rename, Move, & Copy Files" library tool. Here'a quote of my reply in another thread:
...
1. Create a fresh library backup file (it's good to have it if something goes wrong)
2. Disable the auto-import feature (untick the "run in background" setting)
3. Move the files and folders outside MC by using Windows Explorer. A simple drag and drop should move the complete file structure quickly if the target location is on the same disk partition.
4. Fix the library to point to this new base path:
- Select all files and open the Rename, Move, & Copy Files tool.
- Select the Update database point to new location (no file rename, move or copy) option
- Tick only the Find & Replace option
- Find what: C:\Documents and Settings\Owner\My Documents\My Music
- Replace with: C:\Music
...
Naturally you must use your actual paths, no the paths in my example. MC will literally replace the characters in the Filename field so take care that both strings end similarly (either with or without a backslash).
After you have fixed the library you can add it to your other MC instances with Library Manager. Do as I instructed before, except that don't enable the "Clone" option. MC will add the fixed library you have on your flash drive.