Running itunes on two pc's with external hard drive library

Question

Hi All;
I am working with two laptop pc's, a large external hard drive and my iphone. I am in the process of putting my cd library onto an external hard drive and I plan on plugging the drive into either laptop to play my music library wirelessly using apple airplay. Both laptops are running windows 7 and I use the latest version of iTunes.
Initially, I transferred my music off my laptop onto the external drive (following the 'consolidate library' process provided in one of the help menus) and then successfully told iTunes where to find the library on my external hard drive (E:/itunes Music). I then did this with the 2nd laptop. Then I resumed downloading music from cd's.
All of my music is successfully saving to my external hard drive (E:). However, when I download on one laptop and then go to the other, I can't always see all of the albums. I got frustrated, started checking and unchecking things, now I'm sort of lost. iTunes has never been my favorite program.:/
My questions are below:
1. Can I use two laptops and my external hard drive interchangeably?
2. Right now, I get the message 'please choose an iTunes library' but when I direct it to the E: drive and click 'open' it keeps opening into my music files and doesn't open the program. If I try 'create library' I see this:
3. Now that there is a new library, I see this:
but previously I had it set to look like this:
My question is- should I have both boxes checked? Only the top one? What do they mean, anyway?
Ideas, suggestions and links welcome.
Thank you!

Answer 1

Making some assumptions:
The iTunes Library.itl file located at E:\iTunes Music\Music\iTunes 1 is your current/active database
When you run iTunes all your media files can be located and will play
You have free space on your external hard drive - at least as much as currently used for your E:\iTunes Music folder
If one or more of these are not valid, STOP HERE and report back - some parts of the procedure below would be different.
Before starting I would strongly suggest taking a backup of your E: drive as insurance against anything not working as it is supposed to.
Exit iTunes
Open Windows Explorer and navigate to drive E:
Select Organize > Folder and Search Options, then the View tab - make sure that the Show hidden files, folders and drives option is selected
Create a new folder E:\iTunes - this will be the new starting point for your iTunes library
Navigate to the folder where your library files are currently stored (E:\iTunes Music\Music\iTunes 1) - you've already provided a screenshot of this, but with the Show hidden files, folders and drives option selected you should see one more file:
(sentinel is a hidden file that iTunes uses while running).
Select all five files in this folder:
then right-click > Copy or press Ctrl-C.
Still in Windows Explorer, navigate to the E:\iTunes folder you created in step 4, then right-click > Paste or press Ctrl-V.  At this point the E:\iTunes folder should look like this:
Now hold down the Shift key and start iTunes.  You'll get this prompt:
Click on Choose Library..., navigate to E:\iTunes and select the iTunes Library.itl file (that you just copied into this folder).  Click Open.  iTunes will start and show your library with the same content as before.
Select Edit > Preferences > Advanced.  Click the Reset button, which will change your iTunes Media folder location to E:\iTunes\iTunes Media, which is what you should want it to be (ignore the I: drive shown here, yours should be E:)
Click OK - you should get this prompt:
Click Yes.  This doesn't actually move your files, there's one more step.  Still in iTunes, select File > Library > Organize Library... When you see this prompt:
check the Consolidate Files box and - if not greyed out - the Reorganize files ... box.  The click OK.  iTunes will now start copying your media files to the new, preferred location and layout.  The time taken to complete this process depends on the size of your library - for a small one it'll be a few minutes; for a large library considerably more.  Allow the process to finish.
Once complete, your library in iTunes should look exactly as it was before - you should be able to select and play any of your songs/albums.  However, if you right-click > Get Info on any song and select the File tab, you should see that the file location has been updated:
and if you go to Windows Explorer and navigate to E:\iTunes\iTunes Media you'll see a Music subfolder which in turn contains one folder for each artist:
In your case the drive reference at the top will be "My Passport (E:)" and the folders listed will be those for your library.
Successful completion of all these steps should now have brought your library into the "portable" or "well-formed" layout.  Just to make sure everything's working:
Exit iTunes
In Windows Explorer, rename your E:\iTunes Music folder to something like "Old iTunes"
Restart iTunes, without holding down shift.  Your library should be available to you as in step 11 above - however, its worth testing a significant sample of your music just to make sure that everything is in the right place and plays correctly.
One point I didn't cover is the case where the other (older) iTunes library you have - the one where the iTunes Library.itl file is on the C: drive - may be referencing albums/songs that were not in the library that was on the E: drive and that the procedure described above will bring into a more standard format.  If this is the case then there are a couple of approaches that you can use to merge the two libraries - report back if this is the case.
If this last point doesn't apply, you can now go ahead and delete the renamed E:\iTunes Music folder - otherwise there will be a few more steps to go through before you can finally get rid of this.
Finally, once you've completed everything successfully, work out how you're going to create and maintain a backup of your library.  With the approach described above all of iTunes' data is in one place - E:\iTunes.  I would suggest using the method described in turingtest2's notes on Backup your iTunes for Windows library with SyncToy ... remembering that "Hard drives fail.  Always.  You just don't know when its going to happen."
Apologies for the length of these notes - however, based on your description of your current setup I thought it worth going through all the steps to bring it into a more conventional layout.