Actually - scratch all the below. If I try to set my router's DNS back to automatic everything dies as well. So I will have to think about this some more.
BEFORE EDIT:
I'm having issues that are only indirectly related to pi-hole, but struggling to find info elsewhere. I'm hoping somebody has seen similar, or has experience in this area.
Before making any of these changes, pi-hole was working fine with the router configured to use it as DNS and DHCP.
But now I have keepalived using VRRP to provide failover for DNS running on two pi-hole machines. It all works wonderfully if I set the DNS server to individual computers to the virtual IP as a test.
However, the minute I set the router (Netgear D6200) to use the same virtual IP as the DNS server, it kills the whole router and I have to reset it to factory settings. And since it's the gateway, nothing can access the internet during this time. I'm sort of assuming it's because the router is old, but I would not have thought the router would care much about how DNS worked, just where it was. So maybe if I buy a new router it will work?
It's a bit hard to see if anything is going awry in the pi-hole logs at this time, because when connectivity is lost, my Google Nest Home devices spam "connectivitycheck.gstatic.com" and swamp the logs.
As further background, the router does not do DHCP - the master pi-hole does. The whole plan is to allow DNS to keep working should I need to reboot/service the master. During this (brief) period I don't really care that there'd be no DHCP, until the master is back up again. As I say, it all works fine as long as I don't try and set it on the router too. And the DHCP seems to 'magically' hand out the virtual IP rather than the machine one, so "technically" I probably don't have to care about the router's DNS settings.