It appears that what you are encountering is what I call "wind wander", not real trailer sway.
REAL trailer sway is when the trailer starts to sway back and forth in ever increasing arcs, leading to eventual destruction if it isn't stopped. A properly built, properly loaded trailer, on properly inflated tires, being towed by the proper tow vehicle, should never do that. If it does, find out what is wrong, and fix it!
"Wind wander", when encountering cross winds or the buffeting from passing traffic, is simply something you have to live with. I had to put up with it for about 50 miles on the way home Sunday, in our Class A. Even the motorcycles were going down the highway leaning into the wind! It can be challenging keeping it between the lines in those kind of conditions.