That is all correct, to establish a connection and transfer RS232 between two end-points one would need to operate in Sever and the other one in Client mode.
As for device choice, if the device will not be used as a router for WiFi, Ethernet ports, etc. I'd recommend checking out TRB142 - RS232 gateway. It also offers a much more compact design.
Indeed, a second RUT956 may not be necessary, depending on your needs. For using a console via RS232, PuTTY is a great application. To connect to the serial connection, Raw mode should be used. However, if your software requires a COM port to be used for an RS232 connection, there are a few software solutions, that could convert OverIP serial to a COM port. Unfortunately, I haven't used such solutions, so cannot make any solid recommendations.
Hope this helped!