OK I am assuming you have the default gateway on your clients pointing to the pi-hole. Is DHCP enabled on the pi-hole (and disabled on the router)?
If you are showing a large amount of traffic from source IP of the router, this is normal. This is not the router making all these requests. You are basically creating a double-NAT without the NAT with the pi-hole so what you are seeing is your client making a request going to the pi-hole for DNS resolution, then going through the router to the internet. When the traffic comes back to the client, it is hitting the router, the router then has to send it back to pi-hole and then to the client.
I wouldn't worry too much about this. If you put a sniffer on the WAN side and remove the pi-hole but still see this traffic, then there may be an issue.
My router is configured so that it's pointing to my ISP as the default gateway and DHCP is enabled. I'm not using pi-hole for DHCP. However, I do have it setup with unbound as a recursive, authenticating DNS server. My network is setup with a double-NAT; one in the DSL modem, and one in the router. Finally, all of the devices on my network are assigned static IP addresses, and the hosts file on the RPi running pi-hole has been populated so that pi-hole displays human readable names for each device (as opposed to just IP addresses).
pi-hole displays the DNS requests for each device on the network. I can see what each device, including the router, is requesting. When I access the router's
Connected Clients admin page, the router starts generating 100s of request per minute for the following URLs: www.dlink.com, dlink.com, www.dlink.com.tw, dlink.com.tw, www.dlink.com.cn, and dlink.com.cn.
I've just confirmed that no other admin page displays this behaviour. I've blacklisted the latter 4 URLs.