assuming that the pipe serves your mothers property then legally she is responsible for it (along with any other homes which receive a supply off it). That said, water companies sometimes offer a free repair service. phone them up and see.
if the pipe does NOT serve your mother but simply crosses her land then she has no responsibility for maintenance and can phone the water company who are respoinsible for establishing who the pipe supplies and then speaking to them about getting repairs done. The water company does have a legal right to come onto the property to repair the pipe too. whether she expects compensation from the users is another matter.
Our water authority offers an insurance deal and that would explain which parts are your responsibility. Usually the bit that goes to the manhole just outside your house. If you are on a meter, from there to your house, which is quite a long way. I think it is going to be very difficult with all the underground pipes that are going in some areas, to work out who exactly pays for what.