Why are you doing an export? That generates a file to play, not to edit. Double clicking those should do as you first described, open in a player, or possibly iTunes. If that is what you want, then File-->Import-->Movies should work from within iMovie.
If you want to copy the project to another Mac to continue editing it from where you left off, that is a different process that should be a simple drag & drop of the project folder and the related events folders. I think assets used from iPhoto or iTunes maybe tricky though as the project may not know where they are since they are on the first Mac.