This sounds like a good application for serial ports and a "null modem" serial
cable. If your computers don't have any, there are USB dongles which provide a
serial port.

You might download the arduino IDE and look at the source to see how
they do it. I have been playing with the Uno board and found the serial
communication quite good.

I worked my way up from Administrator to Network Administrator for a small
company almost 20 years ago and tried out a "cardless" network to link 3
computers. It came with both serial and parallel port cables. The parallel
ones were much faster but of course that meant you couldn't attach a
printer - a major issue. The idea was a flop as it was much, much slower
than the slowest 10 base 2 coaxial cable Ethernet network. Even small file
transfers brought the systems to its knees for long periods.

When Ethernet cards came down to $150 each we upgraded and never looked
back. Windows for Workgroups provided the networking software.

But that would not be your situation, so it should be quite fast enough for
your needs. You will need some custom software which could be expensive.

Question: Is this secondary system networked or networkable (if you
are thinking of USB connections then it must be located physically
near).

That would be a better solution as you could Telnet or FTP or even VPN
to the system to control it.