Best route from Bozeman to Jackson Lake Lodge
 

Flying to Bozeman Mt on 8/17 and driving down to Jackson Lake Lodge in GTNP to begin our 10 day vacation through GTNP and YNP (flying home out of Bozeman). What is the best route to get to the Tetons..around YNP or through it? Is it a nice drive around the west side of the park (and maybe make a small detour to say..Idaho Falls or is it best to go through YNP? Thanks..
P.S. I know it is very chilly in the ams and pms but is it still too hot to be comfortable in pants all day long?