Yikes! I'm assuming something is actually broken, and the catch is not just stuck due to too much pressure from weather seals and lack of lubrication. It may be possible to partly remove the door card with the door closed, though difficult. Easier with the seat removed, not sure how hard the seat removal would be with the door closed. Main problem removing card is the two forward upper card clips cannot be released due to the dash location. The forward top window clip cannot be released for the same reason. It may be possible to partly release the clips and force the card out with minimal damage. Couldn't say for sure.
Even with the card only loosened and not removed, it may be possible to access the release mechanism and open the door. The seat would need to be out for this to be feasible. It's probably worth removing the card of the good door and examining the lock mechanism to determine how the other may have failed, and how to release the door catch, as visibility with the other card only loosened will be severely hampered.
If it's just stuck, it's a matter of relieving the pressure some how and working the handle until the catch releases.
All this is pure speculation on my part, but I see no alternative. I wonder if a dealership mechanic might know of some special procedure that is not readily apparent, for example, inserting a rod somewhere in a just so manner? Keep us posted how you get on, I'm very curious how this situation came into being. Good Luck!