I tend to not alter or modify anything. It's not that I'm not capable, I just don't like to change stuff that is already there. In your case I would probably not think too much about throwing a duffel bag full of clothes on the floor to hold the door open while driving. If the door rubs on a wall while open I would throw one of the couch pillows behind it to hold it away from the wall.
The only direction of motion that is really a concern is motion from the back of the trailer to the front. This is because the brakes will be the strongest force causing things to slide forward. Next would be acceleration forces, but I only see that as a problem with a big truck and a small trailer. I can tell you there is no way my 3/4 ton Suburban is going to be able to accelerate fast enough to make anything slide rearward in the trailer. After that I think the side to side movement is almost non-existent. Unless you're cornering like an F1 racer, I don't think anything is going to move too much.
Put something soft on either side of the open door while in transit and don't give it a second thought.