Your routers are acting as NATs, which means your client must know the server's public IP address/port number and then the client must connect to that. 192.168.1.100 is the server's private IP address and is unroutable directly.
As far as I know, you cannot tell the router which computer behind it you want to connect to. The routers I've seen (not very many) usually have a system called "port forwarding" that sends all traffic on a particular port on the router to the same port on a particular computer.
Unfortunately I don't know how you will get the IP/port you need. The router is assigning 192.168.1.100:9000 a publicly routable IP address and port number. You need to know what it assigned.
You might be better off posting on some other network-specific forum, as your question is more in the realm of network administration than C++.