Let me check: you server is still somewhere on the net but your client is on a LAN behind a NAT router? In which case the server just sees the routers's internet address as the getRemoteSocketAddress() for all such clients?
In that case, can't you use the ip address plus port number to distinguish between these clients? (The router should map them all to different outgoing port numbers.)
ps: Even so, ~s.o.s~ has pointed you in a better direction