Are you having issues with the Ram towing the trailer? I ask because I'm not seeing any benefit to a backward trade in this case - particularly since you will be losing money.
What is the payload on your current truck? I believe my last 1/2 ton Ram was 16-1700? Figure your trailer gvw is about 7200 and tongue might be in the 850 range when fully loaded (that is not gvw but based on approx. 1200lbs. of gear, about what I carried bringing it to 7000lbs. vs gvw of 7200).
If you have a 1600lb. payload you have 750 for folks, gear and hitch in the truck. That's doable. If you want to carry everything including the kitchen sink you may be at the point of picking and choosing what to leave on every trip.
Trucks. The ONLY benefit in the trade would be to gain a small amount of payload with the 3500. After that I see nothing but negatives.
1) 2 year older truck.
2) 130k on a gas engine = very limited lifespan towing an RV
3) 6 speed tranny in Chev vs 8 speed in Ram - HUGE difference
4) The Ram makes considerably more HP and torque vs the Chev - Chev
360hp/380tq vs Ram 395hp/410tq.
In addition to the above, in a quick NADA search using what criteria you posted and standard equipment it indicates the Chevy would be worth about 21,275 clean retail vs 27,850 for the Ram. There is a reason the dealer is willing to trade straight across. I've never met one (hundreds and hundreds) that gives you a break in your favor
. JMO
Edit: If you can stay within the weight limits with the 1/2 ton you can always install air bags and LT tires as I did. Doesn't increase your payload and in fact will take some off, but it sure stabilizes the softness of the 1/2 ton suspension. Also, in further reviewing the NADA numbers, the dealer is giving you approx. "rough trade in" value for your truck and you are paying the top "clean retail" price for the Chevy. So not really an across the board swap.