While what you are asking for can be done I'm not sure the effort involved will equal the results returned. I am running a setup similar to yours except computer 2 ( and 3 & 4 - I'm talking a ton of terabytes
) are nothing more than dedicated media servers.
Computer 1 is running all the HomeTheater software (xlobby, zoomplayer, ffdshow, usb-irt, touchscreen, etc) and I have never seen so much as a stutter or artifact during video playback. Of course, this assumes that computer 1 is a relatively healthy machine with decent specs, but if you have invested in a RAID array for your storage I don't think you would skimp on the most critical component, the HTPC. After all, its the video processing that requires CPU cycles, RAID storage can be run on old hardware that would otherwise be used as a boat anchor.
Otherwise, if you still want to set it up as you described there are a variety of ways to accomplish it. If the two computers are close to each other you could simply add a USB-IRT and Girder to machine 1 and have Computer 2 control it via IR. The other option is to again place Girder on both machines and send network commands. Lastly, you could map a drive on the remote machine and use batch commands to execute.