as i said previously, i tow a HTT that weighs around 5000lbs. loaded, with my '07 5.3 Avalanche.
i'm surprised you haven't had more issues towing. your trailer is around 6000lbs. "DRY", which no trailer weighs their dry weight.
IMHO, 6000lbs. loaded would be the max i would put my Avy through, especially towing through the Sierras.
you've got a trailer that, loaded, will weigh much more than that, plus all the family and stuff in the Yukon.
i think that loaded, your trailer will be very close to its GVWR.
you really should get it weighed, so you can have real world numbers.