We went through the tunnel in June, 2013, in our Sunseeker 3100 towing a Pathfinder with no problem. We just drove up to the tunnel, the ranger held us until the opposing traffic was clear, and we drove through straddling the centerline, as they instructed.
There are great views through the tunnel wall opening, but I didn't get to enjoy the view. There are only a few turnouts on the entire road big enough for an RV, so don't expect to stop and enjoy it. Of course, I pulled over to let faster traffic pass when I could.
Here's a link to the Zion National Park tunnel web page. It's hidden on the park's home page under Fees and Registration.
The Zion-Mount Carmel Tunnel - Zion National Park (U.S. National Park Service)
Be sure you aren't included in the following, from the web page. Height will be your consideration.
Vehicles over 13 feet 1 inch tall, Semi-trucks, vehicles carrying hazardous materials, vehicles weighing more than 50,000 pounds, single vehicles over 40 feet long, combined vehicles over 50 feet long. All Bicycles. Pedestrians.
By the way, since we had a dog and dogs aren't allowed in most of the park, we had to have a campsite with electricity. Since we were approaching from the east, we stayed at Zion Mountain Ranch RV which is a short distance from the east entrance. It was good, but the ground was just powder. The store across the road had fresh pizza made to order which gave a nice break for the cook. The west side is much more developed and has more RV parks, restaurants, and lots of people. Of course, if you are dry camping, there are campgrounds in the park.
A great thing about staying there was the drive into the park. We are early risers and were driving in with little traffic. There were Desert Sheep along the road three of the four days we drove in.