P rated tires have soft side walls and are not stable/iideal for towing heavy loads. Once sway conditions start the tire flex (side to side) can make overcoming sway conditions difficult. For comparison load range E tires found in most 3/4 ton and larger trucks have stiffer sidewalls, hence handle heavy tongue load sway better.
My guess is that your commander is overloaded, too short for your trailer and the P rated tires make it worse.
I recommend you take your set up to a scale loaded for camping and post your weight numbers here.