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You can certainly change the names of the character but you should also consider changing some of plot line and otherwise removing any identifying information. For example do not mention that this is about your family even if the names are changed
Please note that doing this does not mean that your "greedy" siblings will not try to collect from you (whether justifiably or not). But it does mean that they would have a much more difficult time proving that the characters in the book who will have different names, different settings, different professions, some fictional plot lines etc. are about them.
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If there was no expectation of payment when your mother put her thoughts on tape then you would not have to pay especially if your account is going to be "fictional".
I assume you mother passed away so I'm not sure what standing your siblings would have unless one of them is the executor of her estate. If you late mother has an estate and an executor it may be a topic of discussion.
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