Android Connected to Multiple WiFi
The solution you want is not possible because of both hardware and software limitations. On the hardware side you need a device with 2 WiFi antennas which neither phone has, and on the software side, I never heard that Android supports multiple WiFi connections or antennas. 

Another thing is that Screen mirroring is using WiFi Direct, meaning it connects the TV with your phone directly, not over a router or access point, so your home WiFi shouldn't have any impact on the mirroring itself.