You can ask, but the neighbor doesn't necessarily have to give the key to you. You can start the probate process and get the legal authority if needed.
Every legal matter is fact specific, and there are often nuances in every case. This is intended for comment only, and does not create an attorney client relationship.
Are the pets in the aunt's home??? If so, contact the police department with that information and see to it that the animals are rescued before they starve to death. Does the neighbor know you are her niece? If so, then she may be willing to allow you to enter the home to take care of things that need to be done and to look for a will. Otherwise, assuming you are her nearest living relative, you will need to hire a probate attorney and get an order from the court or letters of administration.
Obviously these are exigent circumstances. The Pet is the first priority. As in any circumstance prudent judgment is the order of the day. If a neighbor has a key, have the neighbor accompany you so that no one is alone inside the house. Take care of the important issue and then look for the important papers. I don't believe you will have a problem. Now if someone is opposing your entering the property - then the animals are to be considered first as for the search for documents a would obtain legal authority.