|I suspect you won't be able to do that unless you can find a USB to RJ-45 adapter that can be configured with TCP/IP addressing.|
Just plugging the unit into your router won't be enough. In order to communicate on the network, it would also have to have an IP address and I doubt the external HDD itself is capable of being addressed directly. If it were capable, it would have an RJ-45 connector on it to plug it into the network.
The simple solution is to plug it into one of the laptops and to share it. Then it can be accessed from the other laptop simply by mapping a drive to it.