I grew up in southern Michigan, which gets funnel clouds quite often, and I've served time (excuse me, "lived") in the flat hell that is Illinois. Once you go through the sirens a few times, the fear fades. Tornadoes are so random and contained to such small areas, it's like worrying about being struck by lightning out of a clear sky. I don't think, however, that there is a way to keep children from getting upset, if the adults around them are getting upset.

So . . .
1. Have a basement. (Living in a mobile home in tornado country is a type of gambling that does not have a good payout. The tornado death rate for mobile home dwellers is 20x higher.)
2. Have a plan. (Go to the basement room with no (or fewest) windows. Duck and cover.)
3. Drill, so it's second nature.

That's it. I have vivid memories of my mom waking my brothers and me up in the middle of the night with the call, "Tornado drill!" I caught a glimpse outside as we headed for the basement, and saw the towering storm, miles-high, coming off Lake Michigan, the sky the color of an angry bruise.

Perspective: Tornadoes are streaky things, but on average only about 60 people per year die in them. Compare that to the 40,000 per year that die in traffic accidents. 15,000 die in accidental falls. Then consider that traffic accidents pale in comparison to heart attack, cancer, and stroke, which take hundreds of thousands of people every year. So, eat healthy and hug your kids. Death from the sky is nothing . . .

Basically, this is an irrational fear. Hard to combat. Information and practice are the only way to get past it.