Is it possible to have a second monitor that is unaffected by fullscreen games on the first monitor?

Is your "main" monitor on the left side? I have a 3 monitor setup with the main monitor in the middle and have noticed that my left screen is fine and dandy even when the middle screen has a superlow resolution, but the right screen is doomed to a life of weirdness (the right screen hence gets the least use and is often used for console games instead of PC use at all).

Try rearranging your PC monitors in Screen Resolution so the main monitor is on the right and see if that helps at all. I'm not sure if there's any way to alter the "handedness" of the resolution screw up, but I've mitigated this problem by using the left screen.

I'm pretty sure desktop icons are basically doomed though--if they're on monitor X and monitor X is too small to hold them, they WILL be pushed away; I solve this by not having many icons the main monitor, personally. Also, if you're having problems with Steam Big Picture mode...I think you're just doomed, I've found no solution to it's weird shifting around due to lower res fullscreen, since it's tied to the main monitor after all.