Problem solved!
I tried a silicone key fob protector. My wife ordered mine from somewhere far away as a Christmas present for me, but I recently observed that they were in abundant supply on the counter at the local Kia dealer's Parts window. It helped a tiny bit, but I was still getting the car alarm going off every time that I had the keys in my pocket and I sat down in just the wrong way.
OK, I've got a bit of Tom Sawyer going on: on any given day, in addition to my key fob and a few other keys, and a wallet, possibly a cell phone, I've probably got a pocket knife, maybe a ball of string, some loose change, a shopping list, perhaps a pen, various other odds and ends in my pockets, and that increases the chance that if I move in just the wrong way, something's going to press on the alarm button on the key fob and set off the car alarm.
My first solution was to stop wearing blue jeans and instead, favor pants that have extra pockets. I can put my key fob in a dedicated pocket that has nothing else in it. That works well, but it kind of limits my wardrobe.
Today I found a better solution. This might not be better for everyone though. Some people actually appreciate the idea that they can push that button and set off their car alarm. You can sort of do that with the solution I found today, but it probably wouldn't work in an emergency. But it probably would work if you were just wanting to use this feature in a parking garage so that you could find your car.
I happened upon this solution by trying to do something else: I wanted to test the battery in my key fob. Page 4-7 of my owner's manual describes how to open the key fob to replace the battery. (The description is too short on details, but I eventually figured it out). It turned out that my battery was fine, but while I had the key fob apart, I noticed that I could remove the circuit board and this exposed the under-side of the buttons, including the one that always sets off the car alarm by accident. There are a couple of plastic tabs that hold the buttons in, and you can work them loose with a fingernail. There's a piece of plastic that lies between the bottom of the button and the circuit board, that remains in place even after you've removed the button for the car alarm.
After removing the button, reassembling the case, and reinstalling the key fob protector that I received as a gift, you'd never know anything had changed. But when I push on the key fob protector for the alarm button, I can't make the alarm go off. If I really want the alarm, I can pull off the protector and push on the plastic where the button used to be, and with a little persistence, the alarm will go off. I can still double push on the door lock button which causes the car to beep once, rather than incessantly the way the alarm button does (that's a handy feature when you've forgotten where you parked).
Hope this info helps any others who maybe fall a little bit into that Tom Sawyer category.