Don't rely on internet alerts for something like that! NOAA weather radio uses encoded warning messages called SAME to do exactly what she wants - turn her receiver on, beep a lot, and and say "Tornado warning" in the middle of the night just like a smoke alarm. The Midland receivers mentioned above will work well. After she gets one, send her here to find the appropriate code for her geographic area:
http://www.nws.noaa.gov/nwr/CntyCov/nwrMO.htm
Input the 6 digit code according to the receiver's instructions, and set it to be quiet unless it receives it (generally referred to as SAME standby mode).
Incident pages are nice, but they require someone else to be awake, hear the alert, transcribe it, send it out, delay over the internet, yada yada yada. They also require the power grid and her internet service to be up. And since tornado warnings can only come from the National Weather Service anyway, why waste minutes getting them? Get her both if you want, but do NOT skip the weather radio.
