Honestly, as annoying as it is, the only real solution is for your mother to drive back to PBI. As you've found, only the renting location can fix an issue such as this.

Given what has gone on, Avis should comp the whole rental, or at least give your mother a free week if the rental is longer than that, to compensate her for her time and inconvenience. That is something your mother can negotiate with the on-duty manager when she returns to PBI to deal with it.