I don't use Unity myself, and can't normally give advice for it. But here it is pretty clear to me, that you don't want to display a workspace inside of another, but just have a application window on top of another application window. Unity simply puts every application to fullscreen.
The idea is not strange at all, as a matter of fact it was introduced in the 60s (December 8, 1968 at San Fransisco Convention Center, watch the recording, its mindboggling: http://chaosradio.ccc.de/ctv051.html). These so called "application windows" have been around in off-the shelf software at least since the 80s. You might even have seen them in proprietary products like Atari TOS, MacOS, OS2, MS Windows, etc... Most Linux Desktop environments handle them pretty well.
With the exception maybe of Unity. But I am pretty sure there is a way in Unity to get windows out of the fullscreen mode. Try grabbing the upper screen bar and pulling it down, or try the buttons in the top left corner of every window or try rightclicking somewhere or ... I don't know. AS I said, I don't use it myself, but you will probably manage.
Once you have your video player in window mode you can drag it to the left and right border of the screen to change workspaces. You can rightclick on it's title bar and command it to stay on top of all other windows, that should be useful in this case.