I have lived in north TX for all my 78 years, the southern end of “tornado alley”. The last time a tornado hit our town was 1948! During those years tornados have hit various other nearby towns and rural areas. But the frequency any of those individual areas getting hit are about the same as our town. Meaning very rare. But when/if it does happen it can be devastating. Or minor. Most tornados in general affect a very small area. And then there are the outliers that are large and long lived.
But tornados occur from the gulf coast to the far northern states to the eastern states. There is simply no way to avoid that when traveling cross country. Best you can do is keep up with forecast of the immediate area you are in or traveling toward. Some campgrounds and RV parks have tornado shelters or designated safe areas. Always ask if that is available, and if not where the closest place is. Have a weather app or weather radio that will alarm if a tornado warning has been issued for your immediate area. Then seek shelter. A tornado watch means conditions are such that a tornado could form. A tornado warning means a tornado has been visually confirmed or radar has detected a circular rotation.
Spring tornados often occur within storms associated with cold fronts. Maybe by watching weather you can trail along behind a cold front instead of being out front in its path. Otherwise try not to focus on it and just enjoy your trip.
Some good reading about tornados.
https://www.weather.gov/lmk/tornadoesfaq