I'm looking for some software that behaves more like Vnc on windows (ie, I can use it to control an existing X session running on :0 and someone sitting at my desk at home can see the mouse moving ...

NoMachine receives a high rating and positive review for its unique, high quality security and performance it provides in delivering remote desktops and applications Rome, Italy September 29, 2010 - ...

You don't need to force Windows-only apps to work on Linux.