You have an active, reachable IP address 10.10.1.2 (production server), and you want to ping 192.168.1.2 (recovery server).
To reach the destination, 192.168.1.2, network traffic flows through the 10.10.1.1 router, which will forward the ICMP packets to the 192.168.1.* network.
If you specify,
# ping 192.168.1.2
and there is no response, this indicates that the ICMP packets sent by the ping command are possibly dropped by the router for the network between the two systems.