I agree--15 miles is nothing, two or three hours even if you're slow. You can't learn much in that time (I've been trying to play guitar for 15 YEARS and I suck).
Also, could the upright riding position of the Simple be making you feel tippy? I know it's supposed to be good for beginners and casual riders, but I hate it. I also dislike those wide high-riser bars. I wonder if you'd be more secure on something that let you lean forward with your hands closer together...a handlebar change is easy and cheap.
I'm mystified that you can't find out frame sizes--I've never seen anything but kids' bikes sold by wheel size, and it's pretty much meaningless for adults.
Have you been to a real bike shop? If not, go. One of our local shops (in a very competitive high-end market) nearly went out of business a few years ago when the economy went south. He changed his emphasis to become a family-oriented shop and takes pride in setting people up with bikes they NEED for the kind of riding they plan to do. He fits them carefully, doesn't move people up to a $1000 bike if a $400 one will do what they need, and he's making money.