SDL grabs mouse (dual monitors)

I have made some progress towards my goal of having two video
cards/monitors, one displaying my SDL/OpenGL graphics, while the other
is used to control it. The problem I’ve run into is that when the
graphics program runs it makes the mouse unavailable to the other
screen, although it is not using the mouse.

My XF86Config-4 has this:

Section "ServerLayout"
Identifier "dual_screen"
Screen 0 "TNT Screen"
Screen 1 “GF4 Screen” LeftOf "TNT Screen"
InputDevice "Generic Keyboard"
InputDevice “USB Mouse” "CorePointer"
InputDevice “PS2 Mouse” "SendCoreEvents"

This makes both mice work, but it isn’t very useful because they both
control the same cursor, i.e. it is as if I have a single mouse. I can
live with this because the graphics program doesn’t need to use the

On the TNT screen I do:

xterm -display :0.1 -e my_SDL_program

and the SDL/OpenGL graphics program runs happily on the GF4 screen, but
I lose the ability to get back to the TNT screen.

Am I doing this all wrong? Maybe I need to have two X sessions running,
but how?