It's all about being seen to be there, I think the telephone link numbers can be counted so it is a way of getting meeting attendance for non attenders.
Ringing on and off is a pain but it is a way of not getting charged. Calls up to 1 hour are free after that time they are charged at an increased rate. Your Mum's price plan probably works in a similar way. If she were to stay on the line and not re ring it would cost an arm and a leg for each meeting. This should have been explained to her properly and she should have been told to redial.
The fact that the brothers are casual about re setting up the link is appalling and shows that they really aren't taking it as seriously as they should.
In our hall we were told that if our telephone had a secrecy function we had to use it, as this is the case and I have no such button it has been pointless me phoning in as the kids make so much background noise it would disturb others. That being said I can think of much better things to do with my time than sit with a phone to my ear being bored brainless.
It is like all things they can say they do something but in reality they only pay lip service to it. No one ever follows through on these things properly. If they really cared the hall in Salisbury would be accessible to the disabled. Don't we have laws about that?