How does firewire enter into the discussion? OMNI does not use firewire(and can't). OMNI must be connected to an Avid HD card(HD, HDX or HD/Native to have any function(beyond passing inputs to the main outs for monitoring hardware sources OUTSIDE of the DAW system. I suggest downloading the manual and having a read to clear up any misconceptions
Here's how I handle 2 computers over the same speaker system; a Presonus Central Station feeds my mains(Genelec 8050's), small speakers(JBL LSR305's) and subwoofer. The Central Station has multiple inputs so I have my HDN system connected(for mixing inside Pro Tools), my computer's optical SPDIF output(for listening to youtube. iTunes or WMP) and my mastering machine uses an Mbox Pro, feeding another set of inputs of the Central Station. A simple button push can swap between 3 sources. Keep in mind that this scenario will work with nearly any computer and interface