I had the same problem with my door. I installed a storm chain as shown in the picture I copied from the Burro
Assembly Manual located in the Documents Center. I also sewed a fabric sleeve and threaded the door chain through it in order to keep the chain from rubbing a big nasty mark on the door when under tow.
I've had to reinforce the wood blocks my door hinges screw into because the screws were no longer holding. I'm convinced the door isn't designed to open 180 degrees because that causes undue flex on the trailer and that the storm chain keeps the door open at 90 degrees.
Of course, the wind will still blow the door shut without an outside door attachment. I don't have a screen door do I can't speak to that.