For a quick exit out of a RV, head for the nearest bath house. We spent many hours in Alabama's - men and women together. People brought in a chair, weather radio, flashlights, water, snacks and we had a instant party in the bathroom. :) State park rangers would come around and knock on doors and that's where they told us to go. Of course, they were constructed of concrete blocks...a wood-frame structure wouldn't be as safe.
If you stay in tornado areas, when you check in ask where the nearest emergency shelter would be. Sometimes they're given on the park maps you receive. These areas are usually well prepared.
We were once on a interstate in Oklahoma getting fuel. Everyone was in the facility watching the news of a tornado quickly approaching the area we were. The truckers seemed to be staying right where they were - in the building. We spotted an highway underpass so quickly drove and parked - with many others. Cars were even driving up the steep slope under the highway and tucking in. Later, folks living in the area told us that is the worst place to park as the wind will funnel right through it. Luckily, the tornado hit a couple miles away but we did encounter extremely large hail so at that point, we were lucky we were parked under the overpass.
When driving the tornado states always stay tuned to weather reports and a weather radio is highly recommended. Stay safe out there.