Last Dec 26, we were at a COE park near our former home northeast of Dallas. Almost a dozen people lost their lives as the tornado came across the area - most of them were on the freeway when the tornado picked up their cars/ trucks and slammed the vehicles into the side walls of the freeway.
We were in a bathhouse at the COE park - I was watching a local TV station on my cell phone. I know the area - and could tell the tornado was headed very close to us. It passed about a mile to the east.
One of the people camped near us stayed in his Winnebago "Because its built strong, and a tornado can't damage it." I asked him how well it would stand up if the tornado had thrown it into the nearby lake?
Tornados do happen, but seldom do they come out of nowhere with no notice. Just be vigilant about the weather. When a front is predicted - keep an ear tuned to there radio. We knew rough weather was predicted and I purposely kept the TV on local TV stations rather than watch a movie on the Dish. Even so - our phones alerted us when the tornado warnings were issued.
Make it a habit to ask about where to shelter in the RV park if a tornado is nearby. Do NOT stay in your rig if there is a tornado warning for the area.
Know which counties you are in, which towns, which are the major highways so you can track how close a storm that might generate a tornado is coming to where you are located.
A much bigger danger and threat to your safety is the other drivers on the highway, any highway, than tornados.
Do keep your travel plans flexible. Some days you plan to travel might be really good days to stay put.