I had this problem with one of my cars once. Turned out that some of the rubber that prevents direct metal on metal contact had twisted inside the latching mechanism between the doors. I ended up basically just pounding on the door with my fist to try and loosen up whatever was blocking it (I didn't know at the time), after about 30 minutes of pounding, trying, pounding trying, I got it open, the shaking moved it just enough to get it unlatched. Then I could see the issue and fix it.
Good luck. It sucks when this happens.