You might think about installing air bags on the rear suspension of your 2500. We had it done on our 2011 2500 Laramie diesel shortly after we bought the truck. It smoothed out the ride considerably when towing. We had it installed at a local shop and had them install a compressor in the truck so we could easily adjust the air in the bags when we were towing vs. when we were just driving the truck by itself. The setup cost us somewhere around $850, as I recall. I don't know what the tow capacity is of a 2013 Ram 2500 diesel, but a 16,000-pound trailer would have vastly exceeded the capacity of our 2500 to tow safely. Air bags, by the way, don't increase either payload or tow capacity.
Dennis and Kathy
And Aggie the Gordon setter
2015 Columbus 320RS
2016 Ram 3500 diesel
Employment was great, but retirement is better