The top hinge of Dometic refrig and freezer doors have a screw and pin hinge that you remove to remove the door or install the door. You seem to have discovered that already, but thought I would confirm your findings.
I have struggled with the same broken hinge that you describe. The procedure I use to remove and install my door is to remove the plastic cap on the top hinge, remove the screw/pin, and then slightly tilt the door and raise up to remove it from the bottom pin, which is stationary. To install the door, just slide the bottom hinge onto the stationary pin of the bottom bracket, (being careful not to tilt the door too much off vertical, otherwise you could break the plastic door hinge), then slide the door under the top bracket and install the screw/pin and then install the plastic cap.
My opinion is the Dometic design of their integral plastic hinge is very weak and a very poor design. Years ago they should have designed a fix for this and replaced ALL refrigerator and freezer doors for this particular model.