Typically your attorney is going to send a notice to her and any other heirs and set a court date. If they want to contest anything, they show up and state what their issue is. Otherwise, the Court can proceed to appoint you and let you get your letters of administration to proceed with the estate.
We typically try to get everyone to agree, if possible. That can avoid a lot of problems later on. The fact that you were the sole beneficiary of his life insurance does not really make a difference when it comes to the appointment. You really will need to contact your lawyer, sit down with them, and have them lay out the process.
It is not clear in what state your father was residing at the time of his death. Presumably your lawyer practices in that state which would be proper. The life insurance designation may be some evidence of your father's regard for you, but the key document is your father's Will and what that Will says about designation of an executor. Since you have a lawyer, and it is good that you do, you should plan your strategy with the aid of the lawyer. On his forum all we can do is second guess the lawyer in charge.
These comments do not constitute legal advice. They are general comments on the circumstances presented, and may not be applicable to your situation. For legal advice on which you may rely consult your own lawyer.
Did your father have a last will and testament? If he did, and if he named you to serve as executrix, then your sister doesn't have to sign anything to allow you to be executrix. You would take the document to the court in the county where your father lived at the time of his death, present it to the judge, and the judge would appoint you as executrix.
If your father died without a last will and testament, also known as dying "intestate," assuming that there is no surviving spouse, you and your siblings stand on equal footing insofar as who has a superior right to serve as admininstratrix of your father's estate. If notice of hearing is given to all siblings and other interested parties, they each will have a chance to step forward and contest your appointment. Ultimately, the judge will decide.
Whether you are sole beneficiary to his life insurance proceeds has no bearing on outcome in the probate/chancery court. Life Insurance is a non-probate asset and is dealt with outside of the probate arena.
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