I would check the trailer axles. I had a single axle trailer once that burned the spindle off due to a seized bearing (no, we don't want to go there
). Took the axle off and took it to a repair shop on the weekend. They fixed it, sort of. On the way home I noticed my truck was always pulling. Watched the trailer and it looked like it was constantly wanting to go to one side. Got home and measured and they either used too short of a spindle or just mis-measured and one side of the axle was a bit shorter than the other. Might be something like that....or just a pure alignment issue. But if truck is OK without the trailer, I would sure be looking at the suspension on the trailer.