Is web player frame rate dependent on the monitor and browser?

I have a client who wants a game delivered on web player (I know... I know.) At work I have 2 monitors. My laptop screen and a giant Dell monitor. I use these for a dual display. I am using Unity 5.3.1. The laptop I am using is a Dell XPS running Windows 10.

Intel Core i7-4712HQ 2.3GHZ

16GB RAM

Geforce GT 750M

When I make a web player build and I have it on the large monitor, the frame rate is around 50 fps on both IE and Firefox. However, when I put it on the laptop screen while running in IE, the frame rate dips down to 20 fps. This happens regardless of whether or not the browser is started on the laptop screen. This also happens regardless of whether or not the large monitor is plugged into my computer. On Firefox there is only a couple frames of difference between the 2 so it's not that big of an issue. The main problem here is that the client needs it to work on IE.

I have tried messing with my nvidia control panel and the web player quality settings without any success. I've decreased the shadow cascades and distances as well as disabled v sync without any changes.

I am using the fps counter script that comes in the standard assets for Unity 5.

This is an issue that I need to solve with the parameters I've outlined.

It needs to be built for the outdated Web Player.

It needs to run at a reasonable frame rate on IE.

It needs to run at a reasonable frame rate on a laptop screen.

Any help would be greatly appreciated. Suggestions about quality settings, boxes I might not have checked, etc would be most helpful.

Thank you in advance.