I am so sorry that you are going through this again. This could have been avoided if your brothers had listened to you in the first place. You all need to reassess the situation, maybe the light will have dawned on them especially if they have to pick up the pieces.

Would it be possible/practical to get extra carers in? Would your mum listen to someone outside of the family if they TOLD her she should go into a home? If they stressed that the next fall (which WILL happen) could be "it" would it make her realise that it's selfish to continue as she is?

Maybe if your whole family were to go on holiday the same week and no care was available your mum might consider having a trial in a home or sheltered accommodation. Once through the door with extra care, fuss and company she'd decide to stay........