Anyone with a streaming pc setup?

Just to clarify, I mean a setup where you have the computer hooked up to a capture card with another PC running OBS. The end result is that you can stream at a higher quality while the other computer can put all its energy into running the game.

Here's the problem I have here: I have an Elgato Game Capture HD. I have my one monitor hooked up to the computer with both DVI and HDMI, the plan is to have both of those displays duplicated. However, the HDMI output automatically disables itself, and won't let me reactivate it. The only way I've been able to almost make it work is if I unhook my second monitor, and the HDMI deactivates as soon as I plug it in again. Anyone else have this problem? Is it a Windows 10 issue?