Or...Something that would be a much cheaper method (if you can find a more basic digital camera with video)......
I'm obviously not aware of the layout of the house, but whatever time of the day she's expected of coming to your Grandfathers house...
Hide somewhere like under a bed or behind something or in the back yard looking through a window, and when she arrives, simply record from that point.
That way, you won't have to worry about recording for a 24 hour period nor worry about her wondering why Grandpa magically bought a computer for himself.
Just another idea. Good luck Matt, hope things work out for ya, pal.
-Jeff