This needs to be done through the probate court. If everyone is in agreement, the judge will generally approve this kind of change.
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Your niece can resign and you can petition for appointment. If you file the documents simultaneously, the court can order the resignation and appoint you as the new personal representative at the same time.
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Your sister will have to prepare an accounting so you will know where things stand when the court agrees to have you take over.
I am licensed to practice law in Michigan and Virginia and regularly handle cases of this sort. You should not rely on this answer. You should consult a lawyer so you can tell the lawyer the entire situation and get legal advice that is precisely tailored to your case.
There is a Petition to file to accomplish this.
You may want to consult with a probate attorney who can, depending on the situation, sometimes save you more costs than what the attorneys fees are. For instance, if there are debts the decedent owed, you may be able to eliminate or substantially reduce them, but you likely won't be able to accomplish this on your own. There is a specific process to follow with certain deadlines for the creditors. It's probably worth at least taking an attorney here up on a free phone consultation.
It is not clear from your question as to whether or not a probate estate has even been opened. If there are no assets that will pass through probate, then the PR does not need to be changed. If she resigns as Trustee of the Trust, then any successor trustee named in the Trust will take over. This is something that you should review with a qualified probate attorney.