Can you disclose what model router ?
I have a model RT-N66U and experienced same as you did.
There is just no way to kill that second DNS IP coming from the router.
Maybe with future firmware updates but still ... its just useless if DNS servers dont hold exactly the same DNS records and its confusing.
To fix, I disabled the DHCP server on the Asus router and replaced it with Pi-hole's own DHCP service: