|To be honest, I don't know for sure.|
I suspect if both router 2 and 3 are capable of wireless bridging then you could probably accomplish this that way. I've never played with wireless bridging so I can't confirm if two other routers could bridge to to a single router or not. This is something you'd have to look into in the documentation.
To be honest, if I were doing this, I'd pull the two cables and connect routers 2 and 3 via a cable. Wireless, for all it's convenience is extremely insecure and inherently susceptible to lag and latency. If your clients will be transferring any large amounts of data, expect that to be slow in comparison to a wired solution. But you have to do what you have to do so I would look into bridging.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.