There are loads of non-shedding breeds such as the Bichon, Bedlington many of the terriers etc without breeding mongrels! However, as has been said, it may be the dander or "bloom" on the coat that causes the trouble so your mother needs to spend time with a particular breed to see if she reacts. Someone I know with the same problem ended up with a small American Hairless terrier, the Mexican Hairless was too big for him LOL!