Welcome henbus! They DEFINITELY do not make the hearty SUVs any more! Our 2004 Yukon XL 2500 SLT with 3rd row bench, 2wd, 8.1L, 4.10 geared, 8600 GVW and stickered payload is 2440# and the maximum trailer weight is 12,000# and GCWR is 19,000#. Stoutest full-size SUV GM ever offered! I searched high and low for one too after my 98 7.4L/4L80E/14-bolt FF/4.10-geared C2500 suffered an early demise thanks to a drunk driver...
Am I recalling the 8327SS correctly at around 7550# dry with a 1K hitch weight an a smallish CCC around 1550#? If so, if you can find one of the rare one like ours, the big Suburban/Yukon XL gasser will get it done. However, you'd likely have more success and comfort with an HD pickup in diesel flavor. Besides, who needs to tote the in-laws???
Given the size camper already, I personally would gloss right over the 3/4-tons and head into 1-ton territory just because of future camper upgrade options and because used 3/4 and 1-tons in these parts run real close dollar-wise.