I had this same bike rack wiggle issue years ago when running a Swagman rack in the receiver mounted on our Explorer but solved it completely by using nylon straps secured at one end to the bikes & at the other to the roof rack on the vehicle and pulling them tight. The same technique would work with any trailer but the problem would be the lack of anchor points on the trailer that the straps could be attached to. The best solution would be to run lag bolts with a loop on the end through the rear wall of the trailer but I personally sure wouldn't want to be drilling holes into any rig I owned just for the purpose of carrying bikes. :E