|I don't even see your problem.|
All routers, servers and workstations are in the same subnet.
How are the routers connected ? If I understood you right, they are connected wirelessly.
So there are two ways connecting the routers wirelessly.
1. router1 access point, router2 repeater mode.
2. router1 access point with WDS, router2 access point with WDS.
Client computers must have an IP address out of the range 10.0.0.100 - 150, DNS must point to your server, because as you described, it's the only DNS server in your network (except router1, which is the DNS forwarder for your servers DNS).
The gateway address of the client computers depends on your configuration of the server. If the server also acts as a gateway, the gateway address for the clients is 10.0.0.2, otherwise it's 10.0.0.4 (router2)
Router2 should have configured DNS server to 10.0.0.2 (your server).
So connection looks like this:
Workstation (WLAN) -> Router2 (WLAN -> Router1 -> Internet
Server (wired) -> Router2 (WLAN) -> Router1 -> Internet
You can use MAC address filter on Router1 to grant access only for Router2, so noone except Router2 can connect to Router1.
MAC address filter on Router2 let's all clients connect to it.