There are two ways a home router can control your DNS:
A) Each client has one DNS server: the router's local IP address. The router runs dnsmasq or whatever to proxy the DNS requests.
B) Each client has one or more DNS servers, with the router's IP address not listed, or listed last.
If you set up B, I think most operating systems will usually use the servers in order, i.e. only fall back to the second (ISP) server if the primary (pi-hole) doesn't respond.
A) Each client has one DNS server: the router's local IP address. The router runs dnsmasq or whatever to proxy the DNS requests.
B) Each client has one or more DNS servers, with the router's IP address not listed, or listed last.
If you set up B, I think most operating systems will usually use the servers in order, i.e. only fall back to the second (ISP) server if the primary (pi-hole) doesn't respond.