You can drive through in your rig with car in tow but don't expect to be able to stop and park as you go through. On one of our visits to Yellowstone, we drove up from Tetons into Yellowstone and out the west entrance to West Yellowstone. It is a beautiful drive even if you don't have the time in your schedule to stop. It a drive through visit is all you have time for, then I would suggest trying to time it to drive through around dawn and shortly there after to give you the best chance to see wildlife from the RV and possibly be able to park somewhere along the way.
