Well, don't do that then, google drive synchronization while streaming? With around 10 Mbps upload your 6 Mbps Stream (which probably is not a perfect smooth 6 Mbps, but rather lumps of faster bursts interspersed by longer breaks) you do not have great reserves.
That might indicate a) you have not much bandwidth reserves in your upstream and once the other user gets active bandwidth get tight and/or b) your router's CPU gets busy if having to run sqm and wifi or c) you have issues, as you run two SSIDs over the same radio. Maybe you could get hold of a router with two radio's so you can use a dedicated channel for going upstream from te 2nd router to the 1st router?