Make the selection on the first menu point to an intermediate menu. Put your transition video as the background on that menu and have its end action set so that as soon as the video is finished, the original "next menu" plays.
An intermediate menu is just a regular menu that's set between 2 things.
An easier way to do this is to drag your transition clip onto the menu and that becomes your selection button. The movie you want to play should get dragged into the project view and dropped on the DVD icon; then specify the end action of your transition clip to link to the video you want to play.