Hi,
Normaly if you do setVisible(false) you will never get any mouse event. I think (but i'm not sure) that if you do setVisible(true); and setOpaque(false); you can get mouse event and your window will not been seen.
If it's not, you can use the Robot class (in awt). You know exactly where your window will appear, you do Robot.createScreenCapture() and specify the location and size of your window. When you make your window visible you draw in it the image you get with createScreenCapture().
Jo
Note : i think you should use the awt.window class whereas JFrame