This sounds like a problem with using an OS, not a java programming problem.
If the program you want to execute is a server that can be connected to the internet, then a client on another computer could connect to it using sockets.
If the remote computers have servers with special capabilities that allow you to ask them to execute a local program you could use that. Then you would need a client that could connect to that server and send it instructions about what you want done.
This reminds me of RMI which is an older framework for working between computers connected to the internet.
Try asking the question here:
http://www.coderanch.com/forums