The reason it told you to have the second router outside the DHCP range of the first router is because if the two routers were to disconnect, and then a computer were to connect to the first router and pick up the IP of the second router, the second router wouldn't be able to reconnect. It's an unlikely situation if you're a) always gonna have the two routers connected and b) if you won't have any devices other than router 2 connected to router 1.

The best advice I can give you is to connect another computer in place of the Xbox and run some diagnostics. You should try pinging router 1, router 2, an external IP address and an external domain name. This will confirm connectivity to router 1, connectivity to router 2, connectivity to the internet and whether or not the DNS is working, respectively. At this point I'd expect you to be able to ping router 2 (the first point of contact to the network) but possibly not router 1.

You might already know how to do a ping, but in case you don't, go to start > run, type in 'cmd', hit enter and then type in 'ping [IP address]' where [IP address] is the IP address of your routers/external IP. If you get "REPLY FROM...." then you know there is connectivity. If you get "Request timed out" then you know there's no connectivity.