I had to do a combination of things like that with a wired and a wireless....
I found some problems with the individual routers and how they would be picky about certain things. I got around some of the problems by NOT using the "WAN" slot, but by connecting the router that was acting as a "switch" directly to one of its data ports. This also bypassed that particular router wanting to firewall all the data.
It may or may not work. Long story short: It was a pain in the behind. I recently replaced both with a single unit that does what I need and it's easier than fiddling.
If you need, pick up a dirt cheap "switch" -- not a port, not a hub. It has no DHCP, it won't split IPs, it just passes data and the router controls it all. Use it as your second device.