I'd like to entertain my 2 y.o. with cartoons while I' trying to work. The problem is that when I change desktops and use mission control it affects second display too. How can I fix fullscreen youtube video to one display? It's getting even worse with fullscreen quick time - the main display is blank... So, is it possible to dedicate one display for entertainment while keeping the other for regular use?
I presume you are not on Mavericks. Multiple Displays support was improved in Mavericks and makes full-screen apps not interfere with other displays:
Full screen applications
With Mavericks, you can use full screen apps on each display independently. Open an app full screen on one display. On your other display, open an additional app as either windowed, or full screen.
You can update to Mavericks which should fix this.