You mention towing with a 2015 GM 2500. one thing I discovered with our new 2015 GMC 2500, is it came with 20" wheels. On our first trip out, I had the tires at 60psi front and rear towing the same trailer I pulled with our 2004 2500 exact same configuration, CC/SB/4x4. while we didn't have sway, I noticed the truck "wiggled" more than the 04 did when going around corners or changing lanes. like it had soft sidewall tires. DW commented. Next trip I put the back at 80psi, big improvement, but still not as stable as the 04. This last trip I went to 80psi all the way around, and it made a dramatic improvement. Now it behaves like the 04. However the 04 was not near as sensitive to tire pressure.
Both trucks were set up with the reese dual cam, I had readjusted it for the 2015 since the 2015 is 2" higher than the 04. had to drop the ball, and readjust the bars to get the front to settle correctly, did all that before the first trip.
Now I wonder if getting the 18" tires would have been a better choice, or if it is just the stock 20" LRE tires have a softer sidewall than the tires I ran on the 04 (Michelins). I was expecting the 20" 55 series tires to actually have less flex and a stiffer sidewall than the 16" on the 04.