Based on the history that you provided, I do believe that an antibiotic in this case is probably unnecessary. I suspect that the NP may have felt "pressure" to do something (provide a prescription) with the holiday weekend.
In this case it is unclear that she even has a bacterial infection. The "little fluid in the ears" is not diagnostic of an actual ear infection. Even if this was an early ear infection, there are a number of studies that suggest that ear infections generally DO NOT need antibiotics.
The incidence of true bacterial sinus infections (acute sinusitis) in children is very low. Most guidelines do not recommend treating sinusitis with antibiotic (even in adults) unless the symptoms last for at least 2 weeks.
I suspect that your daughter is suffering from a viral upper respiratory infection. Antibiotics are likely not going to offer any real benefit. HOWEVER, you must understand, I did not examine your daughter, and I am making an educated guess based on the symptoms you describe.
As for antibiotics and your daughter, we still have the issue of her not accepting the current medication. I have been a strong advocate for physicians actually tasting the medications that they prescribe for pediatric patients, since the taste has such a significant impact on the ability of parents to give the full course of treatment. There are a number of studies that have looked at the taste of antibiotics (finally someone did this research), and confirmed what many of us have preached about.
Suprax (cefixime) and Ceclor (cefaclor) have been shown to score higher on the taste scales in several studies. Here is one of the studieshttp://www.ncbi.nlm.nih.gov/pubmed/10710025