First I look at www.weather.com before we travel to our next stop. They have a section for severe outlook with Torcon index. It looks ahead about 3-5 days. If a front is moving through, it usually moves from the SW to the NE. (not always).
Then we decide whether to stay put, move south away from the approaching storms or go ahead and get to our next stop before they arrive. If you get caught in an area and can't avoid the storms, we use a weather radio with S.A.M.E. technology and leave the county on "all" this gives more warning of approaching storms in surrounding counties. Just scan for the strongest radio signal. I locate the county where we are and make note of other surrounding counties. I ask the park manager where the shelter is located. Learn the difference between "watch" and "warning". In 5 years of full timing we have only had to go to a shelter 3x. Once in Florida, once in Ohio and once in Oklahoma. Once in IL this year we left the park in our toad and drove south to another town and had dinner while the storms passed the campground.