You might look at the option of taking 89 south at Livingston, this will take you through Gardiner MT and to the North Entrance to Yellowstone. We have a 38' Monaco, we weren't towing anything but didn't have any problems.
We were in Yellowstone in 2009 and went to Gardiner for supplies and fuel. Once you get off the interstate all the supply & fuel prices will be higher so it would pay to stock up.
2002 Monaco Windsor 38 PKD
2005 Jeep Grand Cherokee w/5.7 Hemi