We're doing the same, and as I understand it, there isn't anything "on the way" between Tetons and Yellowstone. We're going to bring in 12 days of food with us. Not sure how yet. Looking for ideas here.
I see Walmarts an hour or so out of the parks, so I plan to stock up at them and not have to tow all of that weight across country.
We look at it this way...stock up heavy and that's less vacation time used up shopping.
For the record, we have 3 freezers at our house and could probably make it 50 days or so with the food we keep on hand. Again, I'd rather shop big once a month than stop all the time. We freeze bread and milk too.