Very nice of you to think of something like this for your mother. But what an interesting question as well. One must shift mental gears to consider what would possibly be features that would be beneficial to a first-time digi senior.
Let's get the recommendation out of the way first: Canon PowerShot A1000 IS. And here's my reasons why:
It is a CR recommended buy. It is a simpler model (no manual controls, meaning it's very much a point-n-shoot model requiring no user knowledge about aperture, shutter, etc. settings). It still has a viewfinder, which probably won't be a great one, but the viewfinder may feel more natural to your mother than having to use the LCD to compose and frame her pictures. Of course, she can still use the LCD screen if she wishes. It includes Image Stabilization (IS), which will help reduce the effects of camera shake when she holds the camera and snaps pictures. Is not a sub-compact camera, but a compact so it's a bit bigger and should be a bit easier to hold and (hopefully) the controls would be a bit larger for your mother. And lastly, the camera has face-detection which will help it focus upon people in the pictures she wishes to take of folks.
It is very difficult to find digital cameras with larger controls unless you move up in size to cameras that are known as superzooms or the higher end small digitals like the Canon G11.
Keep in mind that you and your mother will also likely desire to print the images she takes and that may mean trips to a local photoshop (or kiosk at a grocer, big box retailer, etc.). Unless you already have a printer that will print quality pictures you may wish to consider purchasing a dedicated 6x4-inch picture printer like the Epson PictureMate series.
There are similar printers from HP and Canon as well, but I cannot speak to them, but I can of the PictureMate. I own the Snap model and find it to be a very decent printer for quickly outputting 6x4 prints (it only prints 6x4).
In my experience the prints are almost as detailed as those from my local camera shop, but blacks tend to be tinged ever so lightly with green.
With the Epson I would recommend printing regularly as well because the print head needs to be cleaned (a process the printer will do for you) if you let it sit for more than a few weeks at a time.