You sound as if you are up to ninety, and wallowing in self pity and needless resentment.
It's not your DB's fault that your child has medical problems or that you and your DH work so hard and have bills to pay.
Your DB is not necessarily ungrateful or whatever you think he is for turning down your DH's offer of a fishing trip. Maybe fishing is not his thing? Maybe he prefers not to hang out with your DH?
Your DB1 gets very little money and has had certain home comforts provided to him by the grandparents in return for basically staying home and being available for your mum should she need help. Should he sit and stare at the wall all day every day? What he has is not much of a life for a grown man, and there is no future for him in it. Maybe he would give an arm or a leg to have a home of his own, a job, a wife, children.
Would you prefer to see your mum in a care home?
Yes he’s her carer, yes he works hard, but he has it a lot easier than most!
How easy he has it compared to others is neither here nor there. He works hard, you admit, at the job that he is responsible for and he has apparently agreed to do it willingly.
And it’s getting to the stage where he’s letting us (me, my nan , grandad and auntie) do all the hard work. He’s got people to clean, cook and shop for him.
Is he any use at cooking? Does your mum complain about his cooking? How much cleaning is generated by two adults, one a wheelchair user? He can't get out to the shops if you insist your mum must not be left alone.
Are you or someone else rushing in and doing stuff he would do otherwise, or breathing down his neck while he tries to get on with it? Is he the sort that just backs away when there are others trying to do a job that is his?
He wants for nothing!
I doubt that.
Do you just want other people to have to work as hard as you do?
You are complaining about a situation that your mother contributed to - she let the home help go without telling him/her that Bro was off for the evening (and surely the home help could see that anyway?) Your mum could have been in touch with you earlier to give you a heads up.
You are making a mountain out of a molehill. You should talk to the brothers to ask that a contingency plan be put in place if someone wants a day/night off. Getting in touch tonight will probably result in an almighty row, to judge from your posts here. That would not be productive.
You mention so many small niggly things that are quite unreasonable to be annoyed about, on top of big important things like your child's medical problems and your financial situation and being stretched so thin with work and children, and your language here ('killing your brothers') is not warranted .
Needing so badly to vent about every single thing on your plate and doing so on MN is fine as far as it goes, but I would try very hard to take the time to go to your GP to talk about anxiety, stress, and how you could deal with it all better.