You should be able to do exactly as you stated. If you set one drive for one specific region and the other drive for the other region you need then that should work just fine. If you eject that drive though I'm not sure how it will react (I don't know if it will remember it).
Depending on the drive, you can also try flashing it with region free firmware. The Firmware Page is a good place to start to find that kind of firmware. You'll need access to a Windows box though as most firmware is in a Windows format executable.
You can also use VLC - it ignores the region coding. Insert DVD, quick DVD Player, and then startup VLC. This was true for versions before 1.0 at least so it may not still work as expected in the newer official releases.
Another option is to use a program called FairMount which will also bypass the region coding.