Anything you buy should, by law, be 'fit for purpose'. If you were simply sold the phone on the basis that its 'purpose' was to be able to make phone calls, then you've got no right to an exchange or refund.
If, however, the phone was sold to you on the basis that its 'purpose' was to enable someone with arthritis to make phone calls, then the phone is not 'fit for purpose' and you have the right to receive a refund. (You could accept an exchange instead of a refund but this would be at your discretion).
So, it all comes down to the conversation which took place between your mother and the sales person. If your mother made it clear that she specifically required a phone suitable for someone with arthritis, she has the right to a refund (or exhange). If she simply asked to buy that phone, she has no right to either a refund or exchange. The problem, of course, is being able to prove what was actually said.
Give it a go, anyway. Be polite but firm. If necessary, insist on seeing the manager. If you seem to be getting nowhere, mention contacting Trading Standards and also mention that the local newspaper might be interested in the story. Your position ought to centre around your rights. In practice, your chance of getting something done about it actually depends upon your ability to put the retailer under pressure.
Chris