If you'd like to run two separate networks, you will have to carefully configure them to be in two different IP blocks. In general, private IP blocks will not be routable outside the NAT router, so they will be separate, regardless of whether your main gateway is bridged, or you're doing double NATs. Just be careful so that there are no two devices/routers on the same network with the same IP address. Also, you'd likely have to configure them from within the corresponding network, most modern routers will not allow for management from outside the LAN by default.
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