So, if I am understand this correctly, your using another monitor while playing on a laptop?
If that's the case then I can confirm that laptops do not respond well to playing games on a screen bigger than what was made for it, hence the reason most laptops have small'ish screens, other then the obvious reason of them being portable and convenient. Playing games on an alternate monitor stresses the laptop a lot and is often not optimized to do so. Don't get me wrong, there are other ways to get around the situation, but I am not sure that you will find an answer on these forums. For the time being I would stay with your laptops screen.
Quick question: How big is your laptops screen compared to the monitor? Because the bigger the screen and resolution, the harder its working, and the lower the frame rate.