Why do you need 2 wireless routers? You might find that internet doesn't work on a device that's picked up its IP address from the one not connected to the internet.
Unless you really need it, then I would turn the other DHCP server off and let the one connected to your Internet handle the DHCP requests.
Are you sure the switch inside your routers don't support GB? Most ones nowadays do.
If you go from PC at GB to GB Switch to GB Switch to File Server at GB, then it wont touch the router at all. So it will connect through at full GB.