You need the entire libary on the external, not just media.
What are the iTunes library files? - http://support.apple.com/kb/HT1660
More on iTunes library files and what they do - http://en.wikipedia.org/wiki/ITunes#Media_management
What are all those iTunes files? - http://www.macworld.com/article/139974/2009/04/itunes_files.html
Where are my iTunes files located? - http://support.apple.com/kb/ht1391
iTunes 9 [and later]: Understanding iTunes Media Organization - http://support.apple.com/kb/ht3847
Image of folder structure and explanation of different iTunes versions (turingtest2 post) - https://discussions.apple.com/thread/2741246?answerId=13025536022#13025536022 and https://discussions.apple.com/thread/3700206?answerId=17457605022#17457605022
Once you get a complete iTunes folder on the external drive, start iTunes with the option/alt key held down and select the iTunes Library.itl file on the external drive. You will also need to do this with your main computer or the libraries will become unsynchronized.
Alternatively you can make a separate library using the same media on the second computer. Start as you have been doing, let iTunes create a new, blank library file which will be on hte internal drive, set the media folder location in preferences to be the one on the external drive, then add the files to the new iTunes library. Unless you are a super-organized individual, or you don't care if your libraries do not have the same content, you are better off using a single library file that is on the external, not setting up separate library files.
