I have two monitors on my desktop (Windows 8.1 Pro), and I sometimes play older games from GOG or wherever that change the screen resolution for the monitor they're open on. This is no big deal; Windows adjusts and everyone is happy.
Sometimes, however, I have a movie or something open on the second monitor (just a maximized window, not fullscreen). Windows gets the correct resolution set for the second monitor, I can tell because my wallpaper displays normally, but it shifts the maximized window over by a lot based on the altered resolution of the game monitor.
How can I maximize a window, open a fullscreen game/program that changes the other monitor's resolution, and have the maximized window stay maximized on its monitor?