It sounds like the dog is too small for the tail so moving over to the edge of the road when being passed may help BUT when the air from the semi first hits the back of the trailer it's going to send you closer to the edge. With some practice you can time a slight turn to the left when the air hits the back of the trailer to smooth things out but when it gets to the front of the trailer the opposite is going to happen so a slight right turn may keep the swaying down.
The amount of sway is also a function of tongue weight. You may need more tongue weight. Move something heavy from the back to the front of the trailer. If the fresh water tank is behind the axles, empty it when traveling.
