It is great that thewren got those weights.....that is a good start. But without knowing what the Yukon weights are under similar conditions without the trailer hooked up, we don't know if the WHD is setup properly.
My initial thoughts after viewing the weights in post #4:
The trailer is possible overloaded. The 829RKSS lists a GVWR at 7950 lbs. That usually includes the weight of the tongue. Comparing it to the listed weights of my trailer, FR may be figuring a loaded tongue weight of 950 lbs., and 7000 lbs. on the axles......2 3500 lb. axles. If that is the case, both the axles and probably the tires are over the maximum weights.
Without knowing the empty weight of the Yukon, here is more speculation.
With a front axle weight of 3500 lbs., the WDH probably is putting some weight up there, but I am wondering if rear axle weight of 4220 might be exceeding the RAWR (rear axle weight rating). thewren, check the drivers side door sticker.....the axle ratings should be posted there.
Looking at the layout of that trailer, it looks like much of the storage is concentrated in the back end of the trailer. 2 fridges, pantries, wardrobes back there can add a lot of weight. This may cause the tongue weight percentage to go below 10%, when ideally it should be in the 12% area. That could cause the swaying.
I haven't found a good website that lists tow ratings and GCWR for the Yukon, but have found several sites that mention 7700 or 7900 lbs. for the maximum tow rating....properly equipped. If that is so, the the Yukon may be over the tow capacity and maybe the GVWR towing that trailer.
BTW, I changed the subject line to the proper trailer model.