There are several schools of thought regarding rotation. Some things that were not done years ago are done today because improvements nave been made to the construction of tires. Changing rotation is acceptable on radials. Here's what happens. If you choose to rotate tires and change from side to side you will change rotation and position. If the tire was in a position to long and developed a set or wear pattern for that position if it is changed it may start to make a road noise that you will find unacceptable. You won't hear it if the tires are on your TT so no problem. Why rotate tires? As has been mentioned it is not really necessary. The rotation idea is to more evenly wear all tires throughout their life. However, if you have a wear problem address that issue don't move a good tire into that spot to be worn out. Generally speaking on vehicles there are only three things that cause tire wear: teenagers, worn steering parts and/or alignment changes from hitting something. I'm assuming tire pressure is monitored and corrected as needed and that you can control your teenagers. Trailers should have the weight distributed somewhat evenly on each tire so rotation is probably not needed or necessary. That being said, if you want to rotate tires OK it won't hurt anything but keep this in mind. If you take the tires off then you've loosened 20 or so lug nuts that have to be tightened, torqued and checked daily for the first 500-1000 miles of travel.
Happy camping !!!
TeJay