I have a similar situation, several computers that can be used to read e-mail, I have the "leave a copy of messages on the server" selected in outlook, (tools - e-mail accounts- more settings - advanced). my usual computer has remove from server when deleted from deleted items checked, that way if I'm on one of the others I can read and update all the e-mails, but leave them on the server until accessed from my main computer.
only down side is that if I send from one of the other computers, its not captured on the main one unless i cc myself.
no mapping no other software involved.
Rickity