fullscreen youtube video on external display / avoid changing desktops
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.


Source: OS X: Using multiple displays in Mavericks

You can update to Mavericks which should fix this.