Δαφνη Ευτυχια Αρθουρος

So my mother has this shiny, new iMac, and I've got a Powerbook G4. She's got twice as much RAM, a faster CPU with multiple cores, and more disk space than she's going to fill up for a little while. Since I'm hanging out at her house, I'd like to borrow some of that power to speed up some CPU+RAM-intensive tasks.

If I were trying to use an X app, I'd know just what to do -- running an X application remotely is a standard maneuver under X (and one of the niftier aspects of X). But I haven't worked out how to do this with a native Mac OS app that doesn't use the X server. I can use VNC to take control of Mom's entire screen, but that's (a) overkill and (b) a bit annoying, what with the lag in screen updates and radically different screen sizes (and even more annoying if she's trying to use her computer at the time!). I can put off these things until I'm sitting in front of her computer, but when I'm not feeling well, it'd be nice to be able to run things from my Powerbook, in bed.

So ... how do I launch a native Mac OS application with its screen/keyboard/mouse I/O redirected to a different Mac, like I routinely do under X? I'm not the only one who thinks this is an obvious thing to want to do, am I?