You can achieve something very close to this with a virtual PC solution. I tried it with Parallels. For simplicity I'll assume you run Mac OS X on the "real" computer and Windows in Parallels (of course you can run another OS too, I just picked one to keep the story simple).
In the Parallels settings, you can choose which USB devices should be connected to the Mac and which to Windows. If you connect your external keyboard and mouse to Windows, you get a warning that this will disable input from them on the Mac, but this is exactly what you want. Be sure to disable mouse pointer synchronization (in version 5 it's called "SmartMouse"), otherwise you won't see the Windows mouse pointer.
Now you can use the external keyboard and mouse only in Windows, and the main keyboard and mouse anywhere. This is also useful if you want to override something your brother is doing :-)
Doing this in a Mac only environment is currently not possible because it would require changes in the window manager, which is part of the OS. There is a project that does this for the X window manager, but this will not work to control every window on your Mac. TeamPlayer is software that allows you to control Windows with multiple mice, but with the exception of their own programs, you control the computer in turns: only one mouse can give real clicks, the others must wait for their turn.
A complete solution is Userful, but this runs only on Linux, because, as I said, it requires modifications at different places in the software stack and only Linux is open enough to allow this. Microsoft created a similar project: Windows MultiPoint Server, but this is targets to schools and I doubt you can get it. And of course, it only runs on Windows.
I often have to do this with images of plots of data. I use the command line tools that come in the Imagemagick package; I think I installed it on my system with MacPorts. You could also choose to install with brew (brew install imagemagick).
The actual tool you want to use from Imagemagick is the convert tool. If you have your two 320x428 images, say a.png and b.png, you can do
convert +append a.png b.png c.png
to create a new file, c.png, that has the a.png on the left and b.png on the right. Alternatively, you append them vertically with -append (instead of +) and a.png will be on top of b.png. With convert, you can do a ton of other things. For example, you can switch to a different image format for the output
convert +append a.png b.jpg c.tif
This isn't a GUI application, but maybe some others might have a better solution. Alternatively, you could put this in some sort of automator script.
2020-12-10：
I used it on 2020-12-10 and now the correct code is
convert +append a.png b.jpg +append c.tif
Best Answer
The Google Multitask Mode is one of Google's fantastic April Fools jokes. Although technically possible to connect multiple pointing devices (USB mouses, Bluetooth mouses, trackpads, rollerballs, etc.) so far as I can tell, OS X presents only one cursor for all connected devices. This posting at SuperUser discusses this question, and one answer points to this software as a possible solution. YMMV.
Note: my boss just came into my office as I was testing this by using two hands on USB-connected mouses, and my nose on the Magic Trackpad. All three moved a single cursor, as expected. I just got a raise for ingenuity and creativity.