There are numerous antibiotics that can be prescribed to treat ear infections, but no one magic bullet for every infection in every child. Which antibiotic to use in what order varies by region, by physician, and by patient's ear infection history. I often consider starting with amoxicillin again with a child's next new ear infection since it is pleasant tasting, has minimal side effects, works a majority of the time, and is not too expensive. Just because it didn't work with a previous ear infection, doesn't mean it won't work with the new one.
It sounds as if your daughter's first ear infection never totally got better, so changing to a broader spectrum antibiotic like Pediazole for this continuing infection was appropriate. At this young age I do tend to check ears some time at the end of the therapy to see whether the infection has cleared up or not. Pediatricians do have different styles about managing ear infections. I'm sure your daughter's pediatrician would be happy to discuss his ideas with you and to see your daughter, if you'd like.