Does anyone know the GCWR of my father's Dodge, cummins, 2500, 4x4, auto, 3.73 gears quad cab short box?
I don't do Mopars, but as a general rule they are equivalent to a comparably-equipped Ford. So if it's a '99 through '04, then it probably has a GVWR of 8,800 pounds and a GCWR of 20,000 pounds.
But you can ignore the GCWR, because that's not the limiter. The limiter on a Ford F-250 or Dodge 2500 is the GVWR. With one passenger and normal tools and stuff, figure on a wet and loaded weight of 8,000 pounds before you tie onto a trailer. That leaves only 800 pounds of available payload for hitch weight. So that's a max gooseneck trailer weight of 4,000 pounds, a max 5er trailer weight of about 5,000 pounds, and a max tag trailer weight of about 7,275 pounds. (Those numbers assume a percentage of hitch weight of 20 percent for a gooseneck, 16 percent for a small 5er, and 11 percent for a properly loaded and balanced tag trailer.)
So you are right in trying to convince him to use your tow vehicle for any trailer of normal size with any load at all.
My F-250 CrewCab 4x2 PSD weighs about 8,000 pounds not counting the trailer hitch weight when I'm on the road with my 5er, toolchest, cooler, floor jack, sweetheart, and my itty bitty puppydog. Someone with a comparable pickup with the added 400-or-so pounds of a 4x4 would have to leave a lot of stuff at home in order to get the weight down to 8,000 pounds.
My wet and loaded 5er weighs 8,000 pounds. And with the 5er tied on for a cross-country trip, my GVW is usually between 9,200 and 9,600 pounds, or 400 to 800 pounds overloaded. So my next tow vehicle will be an F-350 SRW.