Find a way to counterweight it, so the door becomes more neutral on the hinge.
Look at hydraulic lifters, like on the backs of many of the station wagons, SUV's, and lift backs have.
If it lays flat against the ground when it's closed, put a lever on it that sticks up in the air, mounting it near the hinge side of the door; this could give you the leverage you need to "push" the door open from the top. (this won't solve getting out of the shelter, but you would have more time to do that, too.)
Just some suggestions. Again, I can't see exactly how this is set up, so I can't be more specific.