A lawyer who specialized in wills and estates once said to me, "I'll have to go out of business if relatives ever learn to get along with each other!" I saw his point; family disputes are often the hardest to resolve - particularly when money is involved.
I'm afraid you face a difficult situation, no matter what you do. That's why I hope you'll make this whole situation a matter of prayer, asking God for wisdom to do what is right. Claim the Bible's promise as your own: "If any of you lacks wisdom, he should ask God... and it will be given to him" (James 1:5). Pray too for your sister, that her attitude will change and this problem will be resolved peacefully. However, you shouldn't automatically assume that giving in to your sister's demands is necessarily the "Christian" thing to do. Elsewhere in your letter, you mention how selfish she's always been, and how she cut herself off over the years from the rest of the family (including your mother). Should her selfishness be rewarded by going against your mother's wishes? I doubt it.
As a footnote, I hope your letter will be a reminder to people who may have neglected to make a will, or need to update their wills. Everything we have comes from God, and He wants it to be used wisely - even after we're gone.