Using an external boot drive and the app store I'm trying to setup my MacBook Pro so that I have an internal drive with one OS X installation (Lion) as well as an external installation that boots via an esata card.  Everything is working great except that when I go to install software via the app store on the external installation it finds apps that are installed on the internal hard drive and won't let me re-install them on the external drive.  I'm trying to keep things completely separated, any way to do this?
Boot from the external drive and then eject the internal drive (use Disk Utility or right-click and eject the drive via Finder).

The Mac App Store will no longer see the internal drive when evaluating what apps have been purchased and are installed on the external drive.