You Can Keep the Cousins
Being estranged from your mother doesn't take the rest of them with it, though it takes more of them than anybody warns you about. Who stays isn't random, it isn't a measure of who loved you most. You can predict most of it by how often somebody sits across a table from your mother.
Your cousin two states away can keep you at almost no trouble to herself. She sees your mother at two funerals a decade, nobody asks her where she stands. Your aunt who hosts Sunday dinner gets asked about you every week, she deflects the questions, and her sister wants to know whose side she's on. She isn't more loyal than the cousin is, she's closer, and closeness decides more of this than sympathy does.
Families settle on one explanation of what happened and repeat it to each other. A relative who keeps you has to know two explanations and remember which one she's supposed to be giving, depending on who's in the kitchen with her. Most people won't do that, and the ones who will are usually the ones nobody asks.
The test isn't whether she'll stop speaking to your mother. An aunt can call her every Sunday and still keep your conversation to herself, a cousin can think you were wrong to leave and never once argue with you about it. What decides it is whether what you say to her turns up somewhere else.
You mention something in confidence and hear it back a month later through somebody else. Every call becomes an update on your mother whether you asked for one or not. A relative wants the whole story so she can work out which of you is telling the truth, and you're explaining yourself to somebody who'll see your mother at Christmas either way.
You can keep the relationship and change what you tell her. Say you're not in contact with your mother, that you'd rather not discuss it, and that you still want her in your life. It gives her something to answer, her answer tells you what she's able to do.
The same rule has to run in your direction. Don't use your cousin to find out whether your mother had the surgery, don't send messages through her, don't ask her to prove anything by taking your side. A relative who gets asked by both of you is answering to two people about one estrangement, and the asking is what makes her stop calling. Plenty of the relatives who back away aren't judging you, they're avoiding the questions.
Some of them will go regardless. She's closer to your mother, or she can't stand conflict, or she can't work out how to keep two separate relationships going and decides distance is simpler. It hurts, it also tells you which parts of this family were ever available to you.
You'll get pressure from both directions to treat this as all or nothing. Your family will say that cutting off one person means rejecting all of them. Estrangement forums will tell you anybody still speaking to her should go too. Your cousin and your aunt are separate decisions, and you can make them separately.
You find out for certain when somebody gets sick. Your grandmother goes into care and there's a bill for it, somebody's driving four hours on Saturdays, somebody's covering what the insurance won't. The relatives who tell you what's happening and let you take a turn are the ones you actually have.
You can miss the family without missing your mother. Missing a full kitchen and people who knew you at nine is a separate matter from wanting her back at your table. Keep the cousins who can keep your business to themselves, and let your aunt see you twice a year if twice a year is what she can manage.