If the Pi-Hole is connected on your network and the DHCP server provides the Pi-Hole IP as a DNS Server, all the clients on the network will use that DNS Server.
To set it up as you want you would need to either set up two networks (one on Pi-Hole and one not), or manually assign client DNS (or put the Pi-Hole on the entire network and manually assign selected clients a different DNS Server).
From your description of your network equipment, if the WiFi extender does not have the option of functioning as a router, manual DNS may be your best option with your current setup.
If you use Pi-Hole as the DHCP server, you can use dnsmasq configuration files to allow selected clients to bypass Pi-Hole and use a different DNS Server. This might be the best solution for your setup, as not all clients allow manual DNS configuration.