rear end shakes when pulling trailer

When are you feeling the shaking? Is it on acceleration? Certain speeds? Over bumps? My initial thought is related to the angle of the driveshaft when there is a load on the rear of the vehicle. This load changes the angle of the driveshaft and can cause different harmonic characteristics which can cause a vibration. Driveline angle can be adjusted - but should be set for the most usual operation. If towing is rare, then leave it as it is. If it's the normal regular use, have the angle changed to compensate for the weight induced ride height change.