I am not really afraid of tornadoes—if I were I would have moved a long time ago—but it can be extremely tricky to keep track of both the position of a dangerous storm and your own position when both are moving, especially if you're in a region where you aren't familiar enough with the names of counties or towns to have a good idea of how close a cell is.
It can also be difficult to find up-to-date weather information while driving, since car radios don't receive NOAA weather radio. TV meteorologists are often simulcast on radio, but often rely too much on Doppler displays as a visual aid, making it difficult to follow on the radio. They also tend to fixate on individual cells that threaten the larger cities in the viewing area, and can sometimes neglect cells in more rural areas long enough that it would make it difficult to keep track of their location. (This tendency is why I splurged on a software package that pulls radar data straight off the NOAA network, so I can keep an up-to-the-minute track of individual cells that I am interested in, while the guys on TV are salivating over some gee-whiz storm that has no chance of impacting me.)
At the very least, a roadtrip essential through this region in May would be a battery-operated NOAA weather radio, which I would keep on instead of any sort of music playlist any time I was in an area that carried a Hazardous Weather Outlook of Slight or above. Ideally, I'd either let someone else drive, or enlist a geography-minded copilot riding shotgun. Either way, someone who is not driving should be correlating NWS announcements and warning polygons with a map and the car's current location to advise the driver on when it may be a good idea to stop and wait, detour, or seek shelter.