My fiance wants to play video games in the living room I want to watch tv on my living room TV. I can't stream in the bedroom without the chromecast, and I can't disconnect/reconnect/pause without disconnecting his video game controller.
We're on 5GHz wifi, and our apartment is small so the actual wifi isn't the problem.
It makes me think if a second chromecast might help you in that situation? Then your fiance can play games on the chromecast in the living room and you could stream in the bedroom. Doing both at the same time on one TV is definetely not possible though.
If ... IF... you have Picture in Picture and more that 1 HDMI input... you could PiP the small window for the vidya game (Chromecast Ultra, HDMI 1) and then the big screen real estate for the show (Chromecast w/ Google TV, HDMI 2)? I am not sure if you have a PiP television though.
Can you provide just a little more information? When you say play video games in the living room, do you mean on a Tablet, at the same time as you are streaming TV, or another use case?