Given that the external and primary monitor always has the same resolution, is it possible to have two programs say VLC and a browser open in their separate designated screens?
It is worth mentioning that the external monitor and internal monitor will have to be power cycled, sometimes remaining off for a long period. When they come back they need to remain at their respective monitor, whereas currently they will typically all be moved into the remaining active monitor.
Bonus: Is this possible to achieve by using a desktop environment like Unity from Ubuntu 16.04? It's okay for me to create a custom session as long as the software remains in its given location.

