Try turning off hardware decode of YouTube videos in your browser. The method differs for each browser, and since you don't specify browser you're going to have to search for instructions yourself.
The hardware video decoder is built into the GPU. I've noticed on certain weaker GPUs, decoding video can adversely affect 3D game performance. Turning off hardware decode forces the CPU to do the video decoding, so your CPU load will increase. But most games are limited by GPU performance, not CPU performance.
Another option, if you have a discrete (plug-in) graphics card and the CPU has built-in video, is to plug one monitor into the GPU, the other monitor into the motherboard's video output. That lets the GPU drive one monitor...