Welcome to the Forum...
Very rough answer coming from very few details...
It will probably pull it, but in the mountains you will be running high rpm's.
Bigger issue is PAYLOAD. Rough guess that you will have over 1000 lbs of tongue weight when fully loaded..What you are quoting is a dry weight which is meaningless.
The trailer is a bunk house? If so, that means kids and all their stuff loaded into the Yukon and trailer.
Check the PAYLOAD for the Yukon and don't forget the 1000+ lbs of tongue weight.
Best advice: load up the Yukon with everyone and whatever gear you will put in it and weigh it. Then add in the trailer tongue weight and see if you have enough payload left.