Now, let's step away from this scene for a moment. After it was all over and the full-sized flat was replaced with the dinky, donut emergency spare I went online to see what others had done. On one Q. & A. bulletin board, I found a lot of suggestions featuring rubber mallets, construction boots, driving the car around without the lug nuts to loosen the rim (YOW), and more. But, I digress ...
Now, returning to the problem. A little back story: my wonderful wife is a farm girl, born and raised. She has a no-nonsense approach to machinery. Car companies, don't bother with your shiny sales approaches about how your car will raise the new owner's status, get them noticed at the office, on the road, by beautiful people ... none of that works. She wants to know about the mechanics, about what's under the hood, and especially about how long that vehicle will last. We kept a Mercury Tracer station wagon for most of its nineteen years ... that's what I'm talkin' about. Now, she suggested a little WD-40 on the offending junction between rim and hub. I knew better than to argue ... besides all else had already failed. Out came the little can with the long, skinny nozzle designed to reach tight places. The lubricant was applied to the rim and hub juncture and apparently acted as advertised, penetrating whatever was fused ... Instantly, and I mean instantly, the rim fell away from the hub without any further coaxing. So, my advice to you ... keep one of those small spray cans of WD-40 in your glove box for just such emergencies. It'll beat the heck out of kicking the crap out of your rim and possibly spraining your ankle in the process some dark night on the edge of a deserted highway.
That was truly a teachable moment.
Now, to change the Yaris tire, you'll need to find where Toyota stored the jack, see: http://jsbrookspresents.blogspot.com/2013/04/toyota-yaris-finding-your-jack-and-tire.html
To turn off the Toyota Yaris Maintenance Required light, see: http://jsbrookspresents.blogspot.com/2010/08/turning-off-2009-toyota-yaris.html