I have recently set up the three-pack nest pro wifi, and generally it has been simple and successful.
It connects to the back of a Vodafone Router which acts as the modem and has DHCP enabled. The Nest setup instructions do not provide any guildance on what to do to the modem, so I left it as is. The NEST is using DHCP WAN connection and being served the anticipated internal IP address by the Vodafone router.
I have been surprised to find that most (all?) devices connected to the NEST wifi are still being served their IP addresses from the vodafone box. I know this because the range is 192.168.1.* from vodafone, and 192.168.86.* on Nest. Whilst a surprise, it has not caused any problems until today.
I noticed that the Chromecast devices had not relinked to the new network correctly so ran the usual HOME connection routine. This failed at the end of the process - the chromecasts successfully found the 'same' network as my phone, but were given an 86.* IP address rather than 1.* IP address. This resulted in the HOME process on my phone not being able to see them (wrong subnet).
Clearly, having two devices doing the DHCP is causing problems. Ideally, the vodafone device should remain primary as there are other wired connections going into the back of that rounter/modem in addition to the NEST Pro.
I tried to set the NEST to also use the 1.* range (and carefully set the pools on both devices so they do not overlap), but the NEST does not successfully save this subnet (though it does not error or feedback either, which is poor).
How should I set up the DHCP so that we don't end up with a conflict?
Sounds like you have named the Nest Wifi wireless network the same as your modem?
Modem should be set to bridge mode to avoid double NAT + disable Wi-Fi. More on that:
Then connect devices to your Nest Wifi network only. Both wired and wireless devices. If you need more ethernet ports downstream of Nest Wifi, add an unmanaged switch: