We've had lots of discussions here about a router inside of another router, both in gateway mode. By default home routers are run in gateway mode.
It's not an issue, just have different IP scopes on each one.
Example: Router #1...the one that's connected to your broadband modem, the LAN side of that router is 192.168.0.1, which serves a network of 192.168.0.XXX.
One of the LAN ports has a cable that uplinks to the WAN Port of Router #2
The WAN port of Router #2 is set to a static IP like 192.168.0.11, or simply just "Obtain IP automatically". The LAN side of router #2 is set to a different IP scope than router #1, something like 192.168.1.1, serving up it's LAN of 192.168.1.XXX.
Works fine, I do it all the time. Have a Netgear RT314 right next to me that I build or work on clients machines from, so they're separated from the network in our building, which itself is NAT'd.