So many issues I don't even know which is worse.
First you must use different subnets unless you can actually put them in bridge mode. They all can't be on 192.168.0.x.
You have your second router you say is in AP mode problem is when they are in AP/bridge mode they do exactly that. No traffic will pass the router chip so you will not be able to do any filtering or whatever you had planned. The device will function basically as a dumb switch that has wifi but you have that disabled.
If you run it as a router then again you must have all different subnets on the wan and lan interface
Although it won't matter once you run this as three routers using different subnet all hooked behind each other the nest box can not run DHCP the way you want. It would have to somehow set the gateway IP to be the 192.168.0.1 router but this is not possible on most consumer routers. They always set the gateway to their own LAN IP. OPENWRT can I think set any IP but again to use any of the traffic filter features the traffic must pass through the router software on the box so you have to use a different design anyway.
In any case just hook them all together wan/lan Using 192.168.1.x, 192.168.2.x, 192.168.3.x