These things always puzzle me as well. The hierarchy is important of course. But no need for bones. I used the IK chain tag.
So in this setup you can't move or rotate the whole thing, never really understood why. Maybe if you delete the tag, reposition, and add it again. You can set chain direction in the tag settings. Some produce weird results.
If you want to add the tag again, select the top hinge and bottom hinge and choose Character > Create IK Chain and you're done 🙂
Use the Null it creates to move the door up.
EDIT: I had moved the doors to axis center. Reuploaded with doors in (almost) the same place as your original file 😉
PS: for accuracy you might want to redesign your mid hinge a bit and check position of all hinges because right now now the doors move too far up.