I'm not sure if you can do that simultaneously, because one tuner can only view one channel at a time.
At the moment, the only way that I think this could possibly work is if you use Remote Access to gain control of "home" computer. I know that DVD will not work this way in a network environment. However if you use Remote Access you can watch DVD on another computer.
I think the easiest option for what you're trying to do is get a video sender (click here) but you'll also need a graphics card with AV sockets. Even using this solution, it would not be possible for both computers to use DVD or TV at different times watching different things.