Then they can see that both are connected to a dedicated Tor router in the middle, through its MAC address or other identifier, such as device name.
So they can see that both are connected to the same dedicated Tor router, and thus, they can see who you are that way.
So unless you are confident that you can secure your main home router, then this idea of a dedicated Tor router is hopeless.
You would be better off using a QUBES live disc and ONLY use Tor from the very start.