So, the problem still wasn't fixed, and we decided to take Kia up on their offer to buy the car back. They also offered a pretty good deal, but with all these problems and Kia acting like it wasn't their software, we figured it was easier to just get rid of it. We couldn't have sold it in good conscience anyway.
Guess what? The battery died again right after we got the car back! Looking at the data, it seems like the problem is definitely the software. The only time the battery died when it wasn't plugged in was on a camping trip. We charged it overnight, drove a short distance to the boat launch, and then a couple of hours later, the car wouldn't start. It tried to start, but then gave me a warning about the brakes. I shut it down and called for a tow truck, not realizing the battery was the problem. When I checked, it was super low, like 5 volts. I was confused because I thought the car would start charging the battery itself. Maybe the car's electronics need different voltages for different things, and the charger can't work when the battery is that low.
The worst part is that Kia kept acting like it was some kind of mechanical problem, checking wires and fuses instead of looking at the software. It was really frustrating because I actually liked the car, and after trying a few dealers, I finally found one I liked.