I think what you want to do is to "swallow" the other application's window, or something close to that. Many window managers, and the gnome-panel, for instance, do this to capture programs like xbiff & contain them within a smaller window.

I don't know how this is done, but I do know that your application first needs to find the window ID of the application to be swallowed, by traversing the list of top level windows in the X server and finding the one you're after (usually by checking the X window name, class, resource, etc).

It may be instructive to have a look at the "FvwmIdent" and "FvwmButtonBar" modules in fvwm, to see how this is done at an X toolkit level.