Two In One Switch Connection. But you don't need an internet connection for local wireless play. Any device will be able to connect to any other device on either switch.
Chaos would ensue as systems on the network randomly picked up addresses from each If you want to use two independent Internet connections, you need a "Dual WAN" or "Multi-WAN" router which managed that complexity for you. If you connect two switches together, it will be like expanding your switch - to a point. For more than three Ethernet switches, ring topology is better.
You can connect a single switch on your network to two ISPs.
Since Host A and Host C are in The Router doesn't know that it has two connections to the same switch — nor does it need to.
Ethernet switches perform their linking function by bridging Ethernet frames between Ethernet segments. All you need is two Nintendo How to connect two Switches for local wireless play. Personally, I would connect both switches to the router and to each other, but simply for redundancy.