Is the iPod currently set to use the Manually manage music setting (on the iPod's Summary screen)? If not, the iPod is syncing to ONE iTunes library.
It's difficult for me to fully understand your current situation, based on your description. What you really want is for ONE computer to have an iTunes library with ALL of your songs. Is it possible for you to transfer song files, using external drives or a network connection, and transfer ALL of your songs files onto one computer.
I recommend that you start off with a blank (new) iTunes library on one of your computers. It should obviously have enough local storage to store all of your song files. Run iTunes on that computer, and before you add any songs, open iTunes preferences Advanced tab.
Where it says iTunes Media folder location, if that computer has a large internal drive, you can use the default location. Or, you can use a large external drive that is connected to that computer directly (such as by USB), by changing that location to one that is on the external drive.
Check both of the checkboxes for Keep iTunes Media folder organized and Copy files to iTunes Media folder when adding to library. These settings tell iTunes to organize your song files into the iTunes Media folder, by Artist name, and then by Album name. All of you song files will be organized this way. For example, if you update the Album entry for a song in your iTunes library, iTunes updates the folder structure accordingly.
Now, start adding all of your songs from all of your sources to this iTunes library. Note that iTunes is making a copy of every song file for its iTunes Media folder. Therefore, if you have song files on the computer's drive, after adding to the iTunes library, there will be two copies, one at the song files's original location and one in the iTunes Media folder. You can delete the song files at the original location after iTunes makes a copy in the iTunes Media folder.
After adding all of your songs to create a "consolidated" iTunes library, you can sync your iPod to that library. If it's having data-related problems, do a Restore on it to erase it and give it a fresh start. Going forward, you can back up your iTunes Media folder as a way to back up your iTunes library files.