Hidden agenda? Most likely just bureaucratic rules of the credit union. An account can be held by two people in different ways. If the daughter is a co-owner, the account belongs to her on death without probate. If she just had a POA on the account, it doesn't belong to her, and probate can't be avoided. It would be a good idea to go to a Michigan probate lawyer for advice.
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It sounds like she was added as a joint tenant or beneficiary in which case the account is most likely hers. You need to retain counsel to resolve this issue. Good luck.
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The sister was likely put on as a joint owner. I see CUs and banks do this all the time and it drives me nuts. The sister owns the account(s) outright if this is correct. The sister could give it to whomever she chooses. If she gives 3/4 of it equally to her surviving siblings, she may have an obligation to report each gift to a sibling to the extent that it exceeds the annual gift exclusion amount of $14,000. The gift does not need to reported if each sibling receives less than $14k total for the year. You can split it over two tax years if desired.
Even if it has to be reported, there is no tax on the gift yet. The gift (if more than $14k) reduces the exempt amount of your sister's estate at her death. The starting exempt amount of a person's estate is currently $5,250,000. Most people do not have to worry about estate and gift tax, they have to worry about untaxed income that is inherited.
Talk to a lawyer or have whomever is in charge of the estate talk to a lawyer. If the sister is refusing to share, she could be pursued in court on a convenience account theory. There is too much stuff that can go wrong and a lawyer can earn his/her fee by avoiding pitfalls.
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As noted a above it appears she was put on a a joint tenant making the money hers. You should contact a Michigan probate attorney to resolve the matter.