How do I get my brother to help pay for my mother's funeral?

Who is her executor? That person will be making decisions, after your mother's death.
Why won't your brother be at the funeral home, helping to make the decisions? Because, at that point, I would indicate that Mom did not leave any money. Then, he would have to speak up.
What are your mother's wishes?
What happens if she outlives you?

You will not get financial help from your brother, and tormenting yourself by thinking about his situation compared to yours will only distress you more. He is not interested in doing “the least he could do”.

In your situation I would contact a local funeral home and ask them if they could recommend any agency that could offer you financial help.

Please don’t burden yourself by thinking you need to give her a “nice send-off”. Your care while she is living has been much more important than what will happen in the future.

I hope you see your art as a huge blessing. I’m a musician, also a Catholic, and those 2 parts of my life are so important.

If your brother is wealthy, how do you know he doesn't plan to help pay for your mother's funeral.

I haven't read anything that suggests that your brother has an alt with your mother. You did mention he went ballistic on you when you asked him if you should notify him upon her passing.

Did he go ballistic for you asking him a question like that?

Could he have a policy on her that you know nothing about? Since he is wealthy, he may have plans for the cost of your mom's funeral.

Maybe you should politely have a conversation and see what his plans are.

He’s not obligated to pay for your mother’s funeral and his financial situation doesn’t change that. He doesn’t owe her a funeral—funerals are for the living. It seems like he’s made it clear he’s not going to help pay. At the end of the day you can’t force him to do anything. To be blunt, people who want and or expect a funeral need to make sure they leave behind the money to pay for it. At this point if you want to plan and set money aside, you need to figure out the cheapest option (which is going to be cremation with a simple urn).

your brother does not have an obligation to pay for her funeral. Just as you and your mother have made your own financial and life decisions, he’s made his. You asked and he answered. Don’t try to guilt him and don’t try to compare income levels. Parents decide what to help their children with financially and they shouldn’t do it with the expectation of a return on their money. If they wanted a return on investment, they should put their money elsewhere.

Alva is spot on.

Your brother may or may not have some unresolved issues with mom and that's what's holding him back, or he simply may not feel any desire to be involved. You can't change him, and guilting him in to this? Probably won't work.

Write him ONE letter, have zero expectations about what he will or will not do, and then let it go.

If you feel responsible for mom's burial, etc., go talk to a mortuary and pre plan and pre-pay for as much as you can. Use MOM's money--not yours.

You do NOT need to go 'top of the line' to have a nice memorial. In fact, should mom die during COVID, you can't even HAVE a funeral, thereby passing up a lot of the cost. Don't let guilt make you buy the $20K casket or the thousands of dollars in a headstone, etc. Doing it beforehand when your head is clear will pay off in spades when the time comes and you are grieving, yet trying to make big decisions.

Does mom have ANY discretionary income that will help with the costs?

This is a hard talk to have with a parent. Your relationship with your mom may be a 180 from his. Maybe he has feelings about her that preclude him making 'kind' decisions.

Sounds like you have never had much of a relationship with him, this shouldn't surprise you. But we are always surprised when people don't stand up.

Your last sentence tells us all; it is unlikely your brother will help.
I am so sorry for all you have gone through. But now it is time to make your OWN life as good as you can. You have taken care of your Mom. What her funeral is will matter nothing. You can do her honor in another way. For my own brother I make a journal, decorate and collage letter to him that comfort me. It isn't about throwing a whole lot of money at a mortuary.
I am sorry for the bad things that occurred in your life. But those things aren't about your Mom or your brothers. Your brother doesn't even wish to be told when your Mom dies, so why would he pay for a funeral.
You can make one last ditch effort. WITHOUT ANY ACCUSATIONS write your brother a gentle SHORT not in a beautiful card. It should be very short. As in "Dear Brother:
When our Mom dies I wonder if I can ask if you would be willing to assist me with her burial costs? I do not have the funds to do it, or I would not ask you. Thank you so much. Your Sister."
NOTHING else. Any telling him about miseries and sacrifices will simply make it easy to write you back "Nope!"
With a few short sentences, if he denies you and your Mom, you will know all you need to know.
We cannot change other people.

All you can do is ask. I would avoid making comparisons of your finances to his. Ultimately, he’s an adult and free to choose how he spends his money. Hopefully, he will help, but if he chooses not to be prepared to have a small service with a small budget. My dad’s funeral a few months ago was outdoors and small, and it was fine