creating child window for fullscreen app

I'd like to open a child window with a directx game window (UT2004) as the parent. When the game is run in windowed mode, everything is good, but when I switch the game to fullscreen the window opens but doesn't show. I know it opens because if I switch game to windowed mode, the created window is there.

I think the game is drawing over the window in fullscreen. I solved this in windowed mode by adding WS_CLIPCHILDREN to the game window. How do I solve when game is fullscreen?

Thanks!