If you use an app like RethinkDNS, it will allow you to run multiple, simultaneous VPN connections and then choose how you want to route your traffic.
I have the same situation as you. I run two VPN connections. One to home and one to a VPS. I route all traffic to 10/8 to the home VPN, certain apps to my VPS VPN and then the rest of the traffic via the local connection.
RethinkDNS also does local DNS filtering and allows you to specify which DNS service to use. I run my own DoT service that backs off to the PiHole at home.
You will need to be more specific on your configuration for us to provide a more comprehensive response.
I have Pihole configured with Mullvad as the primary upstream DNS provider (albeit with DoH).
Just make sure you're using IP addresses for the upstream Mullvad DNS servers since you won't be able to resolve their names without first having DNS (i.e. chicken-egg).
... anyway...