Anne, dear, I have a suggestion that’s somewhere in the middle. It’s only applicable if you think it was unfair of your father to leave his money as he did. (It was HIS money, and he had the right to do what he wanted with it.)
I don’t know if you have them, perhaps in your tax tecords? See if you can gather reciepts for what you spent on your father’s care. Add in non-medical expenses such as furniture, loss of income, and a wage for yourself equivalent to what in-home care would have cost.
Subtract that from the total amount your father left to you and your sister.
Divide the result in two, and offer her the difference, if any.
I tend to agree with those that say you owe her nothing beyond what your father left her.
… You could just say that you’ll remember her in your will - but not say how!
