You can use the second Pi to serve a subset of your network. Assign it a static address, and manually point selected clients to it. Some users do this to create a kid-friendly internet filter. The second Pi could have more block lists to remove adult content, etc., and you could configure it’s upstream DNS servers to one of the filtered DNS providers.
Another easy option if you just want redundancy is to move the DCHP function back to the router, give the second Pi a static address, list it as the second DNS IP on the router. Then the two Pi’s run in parallel (how much load is distributed is dependent on your network and router). If either fails, the second automatically takes over. If you do this you will typically want to run the same block lists on both Pi’s, and synchronize the white and black lists at some periodicity. Sync can be done via teleport.
A third option some users choose is to have each Pi serve DHCP, but set their DHCP ranges so they don’t overlap.