The Nikon L35AF and L35AF2 (One Touch) are both excellent cameras, with minimal controls and excellent picture quality that can usually be found for less than $20. Also consider the Canon AF35MII and AF35ML (this is the one with the 40mm/1.9 lens), either would also be a fine choice for one used to shooting with disposables, as would be the Olympus AF-10 Super.
I have no argument with any of the other cameras mentioned in this thread, I own most of them and they are all fine film cameras, but they may be more than your mom really needs.
If you really want something that is high quality with minimal controls, maybe consider a fixed-focus camera? I can recommend the Nikon Sport Touch (AW35) in this category. Rugged, weatherproof, quiet, with an excellent lens and a focal distance of 3 feet to infinity, it is a perfect snapshot camera.