It's easy for us to make 'helpful' suggestions but family dynamics can be incredibly complex and difficult to change. As long as your brother has your mother's ear and is able to manipulate her so she agrees with whatever he says, you are pretty much scuppered unless you make a Big Fuss, which might result in a permanent rift.
Your brother is a bully and is trying to control everything. Obviously he thinks you should not be joint LPA. Mine was the same and tried to insist on keeping mum's finances secret on the grounds he had 'promised both mum and dad he would never discuss their finances with me'. That was BS! Mum disliked him and had always been open with her finances - she'd show me statements, her will, etc, every time I visited. Brother didn't visit so only got involved when I moved mum to a care home. Besides, mum had made us joint PoA and brother's opinion does not trump the legalities! In the end, I had to make the Big Fuss to get to see the money situation - threatened to report him to the Office of the Public Guardian and get him removed as LPA for acting illegally. The threat worked and I'm pleased to say he was compliant/co-operative after that.
But I have never got on with my borther and so there was no relationship to lose. You are very keen to keep things going with your brother and your mum so I can easily understand your reluctance to 'rock the boat'. However, he can't have you removed as LPA. Your mother does not have capacity and besides, you haven't been involved with the money at all so he'd have no grounds - they only remove LPAs who are acting wrongly. (So you would have grounds for his removal (i.e. he isn't acting in your mother's best interests) but he doesn't.)
But things can't continue like this and your mum is only going to get worse. She may not accept help now but she WILL need carers sooner or later. (Needs them now!) I'm afraid I'm also somewhat suspicious about your brother's motives. Why on earth would he not want your mum properly looked after? There is no excuse. As your mum would be self-funding, I can't help wondering if this is about money. Paying for carers would soon start to make a dent on that 400G. Is he hoping that without help, she will just die, and sooner rather than later? I know that's a terrible thing to imagine but is it possible? I don't know how long your mum is likely to live, but if SS got involved and decided she needed 24/7 care, they might move her to a care home 'in her best interests' because she was refusing help at home. That would cost at least 50G per year and maybe your brother has his eye on that money.
Sorry if my comments have caused offence - obviously I don't know you or your brother but from what you've said, it would seem he has ulterior motives and clearly isn't putting your mum's welfare first.