Let me call the Ubuntu system "the server" (runs gnome) and the X server "the terminal" (which uses Tom's window manager).
I can run the command gnome-session on the server through a ssh tunnel from the terminal, but that makes the server control the entire real estate of the terminal.
What I wish to do is to run the server's window manager in a window on the terminal. A method to run another instance of the server's window manager in a server window will also achieve the desired result (as I can run that window through a ssh tunnel).
Another way to put this question is, how to run the window manager of a headless system in a window of another X11 server.