Elise,
Two displays: yes, that's possible (eprime 2 pro)
Two keyboards: no (although combining different types of input devices is possible)
Creating a parallel task in a single script will not be trivial, if not impossible in most cases.
So, a single computer set-up would not be my favourite choice.
Two separate computers will be more flexible. Communication between the systems can be done in several ways. A direct serial (RS232, using nulmodem cable) or network (TCP) connection is possible, but may be difficult to do if you're not already experienced with E-Basic scripting. Handling the (asynchronous) data stream will be the most difficult part. (Depending on the complexity of the exchanged information.)
Another option is to create files on a network share that can be accessed from both computers. Although this seems easier to do, this not a very elegant and reliable method.
In very specific cases a mixture of both methods might also work. For example: a simple TCP data stream for sending events or triggers, and a file share for exchanging more complex event related info using files.
Best
Paul