Originally Posted by texasredneck
.... I thought there might have been something to do with the rearend of the jeep.
You could check that the rear swaybar is still on the Jeep. If it were removed, you'd get some nasty body sway on turns even without the trailer on.
Also, be sure the trailer tires are in good condition and have the correct pressure (as well as correct pressure in the Jeep tires) and that all the suspension parts of the trailer are in good shape as well as the wheel bearings.
I've towed a small dirtbike (3 rail) trailer many times on the Jeep. A couple times with a battery operated golf cart on it (which is a lot
heavier than a quad), and never had any sway problems. Having a LWB Jeep helps, but I'm still guessing it's more trailer issues than Jeep.