"I already have discussed it with her. She says that my cousins have already paid her back what they owed her. The thing is, what they owed her before was a small amount, just a couple of hundred each. Fair enough. My fear is that she has now set a precedent for them that she will pony up money for them for whatever they need when they ask next. And make no mistake, they WILL ask again. When my cousin decides to leave her husband, I'm sure it's my mother who will "loan" her the money to get out of a bad marriage. But given the history between my cousin and her husband, she'll likely go back to him again (as she's done before).
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You are way too invested and knowledgeable about your extended family's finances. Try this: Drop the rope. Quit informing yourself about your aunt's bank account, and what date your uncle gets a check. Your cousins? Their finances are their business, same as your mother's is her business. Stop projecting your fears into the future and finding ways to make this part of your life.

Ask your mother if she wants you to help set her up with a meeting with a good financial counselor. Set it up if she agrees and DO NOT GO to the meeting. Let your mother adult, and accept that she is not going to adult the way you prefer -- same as you didn't make the choices she would prefer when you became an adult. Then let her deal with the consequences of her choices WITHOUT GETTING INVOLVED.

Her money, her business. When she calls to talk money, change the subject or tell her that you can't discuss fiances with her any longer. Setting that boundary, to guard your own emotional health, is going to be a lot easier and more healthy than trying to force your entire family to live the way you want them to live, sensibly and frugally. Sit back, drop the rope, and quit judging everyone.