When you accessed your external drive iMovie library on your newer Mac it automatically updated it for the newer version of iMovie being run by your newer Mac. Thus your library became a library that was created "using a newer version of iMovie". That would make the library inaccessible with your older Mac running an older iMovie version.
On your older iMac you might try looking into the iMovie Backups folder to see if you can open an older library that you can access with whatever version of iMovie that the iMac is running. I believe that the backup library will open on your iMac and not the external drive, but not sure about that.
To get to the iMovie Backups folder, follow this file path from the Finder menu:
Go/Home/Library/Containers/com.apple.iMovieApp/Data/Library/Caches/iMovieBackups
When you get there you will see a list of previous backups of your iMovie library. Click on one dated just before your issue started. iMovie will open in that library. Navigate to your projects browser (where your projects are displayed as icons) and see if your projects are intact.
On your older iMac you also could try updating your iMovie version to the one that your newer MacBookPro is using. Or possibly you could copy the newer MacBook Pro iMovie app to your older iMac and see if that would make it compatible. Copy it to a different location than the older iMovie app and back up your older library just in case you might need to access it.
If you keep a Time Machine backup of your older iMac you could copy the external drive iMovie library to the [EDIT] older Mac and see if you can restore the iMovie library to the older backed up version that is compatible with the iMovie version that the older Mac is using. Restore it to a different location than your updated external drive library, so as not to overwrite it. Or perhaps you have an older iMovie library backed up somewhere else that you could use with your iMac's iMovie version.
-- Rich
