That is a driver problem.
I once had a 2 monitor setup (on a single video card, first with an x800pro then a 8800gt) and what would happen, for example, is that if I switched my MPClassic from one screen to the other (after a file had been opened), it would either go black or be very choppy. The solution was to start the program, move it to the monitor I wanted to use and then open the media file.
This behavior would be different depending on the drawing mode selected (dx7 or 9, windowed or not, etc...) in the option menu. I suggest looking into it and trying different options until you find satisfaction.