I have a 27' travel trailer that I back up a steep driveway to park. When I had my 01 Suburban I just put it in 4-low. It hardly worked the engine or transmission. I now have an 05 Denail XL with all wheel drive. It works it a bit getting up the hill. I think what works best with that is getting it turned into the driveway and lined up before going up the hill. Then I just gun it and back up the hill. This works the Denali a lot less than trying to do it nice and easy.
---------- Post added at 01:13 PM ---------- Previous post was at 12:55 PM ----------
Going back to the original question, here is a link to a towing guide to see what your capacity is:
http://coachmenrv.com/owners/guide/
Good luck with a cross country trip. I usually get around 8 mpg pulling my 27' that weighs about 6,500. I have gotten as low a 6 mpg and just got 10mpg a couple weeks ago on a 200 mile trip. I had a 20-25 mph tail wind most of the way. That was nice. I don't know how much of a difference the shorter wheel base of the Tahoe / Yukon makes, but it might be a bit squirly with a trailer that big, especially if there is a strong cross wind.