Router #2 is also plugged into one of the out ports on Router #1
If this is the case devices on connected to router1 should be able to access the server if you add a static route in router1's routing table and make the appropriate changes to router2's firewall (or turn it off completely). In order to provide further guidance you'll need to provide the model of both routers and the "WAN" address of router2. This would not impact the usage model of internet services for devices connected to router1.