When I worked on my previous game Catyph, there was a video transition between each scene (it was a Myst-like game in first person view).
I remember I had a lot of issues, and the video was not playing as I wanted (even in the final version of the game there's still a short freeze as you can see in the playable demo
However I managed to get a nice result in the end I think. Most important: make sure your video is in the recommended VS format (mkv, etc), which changed a lot of things for me.
You can try the following thing too: don't play your video "at the end" of the current scene, but play it "at the beginning" of the next scene (which you probably tried already).
There should still be my questions somewhere on the forums about this. Hopefully you'll find a solution. Good luck!