Perhaps I don't fully understand the problem you are seeing. "Clients cannot resolve any hosts".
The debug log shows that the Pi-Hole received more than 33K queries in 24 hours, most of them from the router. The router is the DHCP server in your setup, and almost all the queries are shown as coming from the router. The router isn't making all those DNS requests - what you are likely seeing is the queries from all the connected clients appearing to come from the router.
Please clarify the problem you are experiencing and why Pi-Hole only works on the Pi you installed it on.
Also, please post the outputs of these commands from the Pi terminal:
echo ">top-domains" | nc localhost 4711
echo ">top-ads" | nc localhost 4711