Wow - thanks all for the reassuring replies! We happen to live in an area that doesn't much get natural disasters - except for our plentiful snow. ;)
We've been waiting for retirement (yee-hah!) and want to get on the road as soon as possible. That's why we want to head south to get an early spring.
As much as it would be great to have flexible travel plans as suggested - there are an awful lot of campgrounds that are already getting reserved up so we have to jump in now. So far we've got reservations for Nashville (Seven Points) and Gulf Shores. We do have short travel days planned, so we can adjust what time of the day to travel, and of course if there are tornado-y storms around we'll have to really adjust and lose some reservation money.
I have read a lot on here about what to do when tornadoes are around and we will certainly do the utmost to save ourselves, but we would be heartsick to lose our rig.
Thanks for the tips on weather radios and apps for the phone. Also for tips on what not to miss - we are *so* looking forward to this trip!