We've taken this route several times with the most current being last September. We were coming from Greybull, so we spent a couple of nights at Buffalo Bill Cody State Park, then drove into the park through the East Entrance. It's really nothing to be concerned about. The tunnels are no problem. Our FW is 13' 5" (if I remember correctly. We have a label taped to the inside of the window on the driver's side as a reminder, including the rear height for another point of reference), but as one poster here said, semis drive that route delivering food to Yellowstone NP. You do have to take it slow though heading into the park due to traffic and speed limits and more so in the park as they speed limit is strictly enforced. The roads are excellent, plenty of shoulder and just inside the gate is a wide pull over with a restroom in case you have to stop, which is what we did. The KOA in Greybull is really nice as is the one in Cody, but we've only seen it driving by. You may want to adjust your stops so that you head into the park from Greybull, hence early in the day. If you try to make it all the way from Devil's Tower, you'll be arriving late afternoon. According to MapQuest, Cincinnati to Yellowstone is a little over 27 hours. You may want to allow 4 days instead and break it up that way. I know that towing is tiring and can be stressful. My husband and I switch off driving when we have a deadline to meet, so I know it can be tiring. Take your time so that you enjoy the trip and if possible switch drivers.
Also, you didn't mention when you were going to Yellowstone. The time of year makes a big difference. For us, we always travel in September. Less crowds and it allows us the flexibility of changing our minds mid trip and not worrying about getting a place to stay. When we went to Buffalo Bill Cody last September, we just drove in, no reservation and a lot of spots were empty, so we had our pick of hook ups or not.
