This is a common circumstance, and the law contemplates that a successor administrator may have to be appointed. The process of appointment of a successor is very similar to the process of appointing an administrator. You file a petition giving due notice to all the heirs and other interested parties, and the heirs who have not acknowledged service or consented to the appointment of the successor have to be served by process and they have an opportunity to object to the appointment. You would be well advised to work with the lawyer that set up the administration in the first place, and if none was used, to at least consult one before attempting this on a "do-it-yourself" basis. You will maximize the value of the house to be sold if the buyer receives clear title with a minimum of hassle. Good luck.
If an alternate was named in the Will then that's the person who the court looks to.
If no alternate then the Court decides who will best carry out the deceased's wishes and may require the posting of a performance bond.
Contrary to what many believe, lawyers are not involved simply for attorney fees. Most courts prefer lawyer involvement because they know that lawyers will timely file the required documents and follow up with the court or their licenses are on the line. Consult an attorney in the state where the property is located and where probate is pending (if different). Good luck!