@ blueprint,
Sorry I didn't find this thread earlier. Hope you were able to locate the medical supplies you were seeking. A local medical based charity to which I donate, Heart to Heart International responded immediately to the need in Central Arkansas with their medical semi and team. They should have been able through not only their on-site medical, but the kits they distribute (sponsored by Johnson & Johnson), to alleviate some of the strain on your local First Responder networks.
I've lived in tornado alley all of my life. We used to watch the tornados come across the Kansas plains, destroy businesses a couple miles away, pick-up, and come down a couple miles on the other side in Missouri to continue their destruction. I've gotten to the point that I can read the greenness of the sky and feel the barometric pressure drop and know that there is tornadic activity in the area. This usually occurs a minute or so before the official sirens go off.
I've been in two situations of a near miss from a direct hit by tornados. Property damage to the structures occurred both time. Once I was in FL, in a trailer, and it was a wild ride (middle of the night and I was awoken by the sound of a train (tornado). The other was in my current home, not typical tornado season and I had unplugged my weather alert radio, and it was the middle of the night and I was awoken from my sleep by the sound of the wind. I argued with my normalcy bias about 30 sec. . By the time I made the bedroom doorway the house was shaking and I held onto the doorway frame as I felt the pressure inside the house change dramatically, by the time I made it down the stairs to the basement entry, it was over. While the local weather station refused to call it a tornado, or even a micro-burst, the length of the path and signs of destruction were unmistakable that it had been an EF1 or EF2 passing directly overhead.
That said, I am of the opinion that when the time comes that you are debating whether it is time to go to shelter, it means you should already be there and are allowing your survival instinct to lose the argument with your normalcy bias.
I'm glad you and your family were safe this time. Betting on technology when your gut says maybe it is time to send the family to the shelter isn't one I'd be willing to take a second time. It would be a horrible bet to lose. "Better to be safe than to be sorry" comes to mind. Just my $0.02, YMMV.