I assume from your summary that your father has died. If that is the case and you have been appointed by the court, then YES, you absolutely have the authority to have your sister evicted. You may want to contact an attorney about doing this, because there are lots of procedural requirements and if you miss a step, you can be forced to start over.
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Actually, the answer to this question is different in North Carolina than most other states. In North Carolina, where there is a Will, the North Carolina real estate (including the home) is owned by the beneficiaries of the Will and not the estate upon the death of the owner. This means that you as Exeuctor have no authority over this home. Instead, the individual or individuals who inherit the home under the Will own it, with no action of the Estate or Exeuctor, and those beneficiaries have the authority to evict a person who is not an owner and does not have some other (contractual) right to the home. In turn, I would say that your Sister has no direct obligation to pay the untilities, but likely has an obligation in fairness to pay rent for the period of time she has occupied the house. I would suggest that as Exeuctor you might have a duty to notify the beneficiaries under the Will (which I suspect includes you, individually) of these facts and would encourage you to seek the advice of a North Carolina attorney to assist.