Last night I tried (with no success) to set up a dualscreen (I managed to do this) and have a fullscreen player session on the "secondary" screen (the "main" screen was my laptop with maptool, dm genie, token tool and IE to make tokens "on the fly") but couldn't do that.
When I got the player maptool go fullscreen, it would always be fullscreen on my main screen (so I got around it by making the windowed player session as big as possible, but still...)
This sounds like you possibly don't have your secondary display set to "Extend my Windows desktop onto this monitor" or that you don't have the displays configured for independent resolution.
Depending on the video chipset the configuration varies a lot. With nVidia you want what they call DualView. Both displays are configured independently and have their own resoultion.
The important part is that you do not want to mirror or clone the displays. Most laptops default to mirroring the displays as that is how they are typically used in presentation environments.
You don't want that because you want the player client to be independent from the GM display.
Unfortunately it can be a bit of a pain to get some laptops and their chipsets to do what you want.