Here is my $.02. I'm a dude, but I can somewhat relate to her behavior.
When I got out of graduate school, I went to teach courses at a university. I kinda thought "professional dress" was a stupid concept. (I still do actually, but I digress...). So I dressed fairly casually, and since I also looked pretty young for my age my students showed me a lot less respect than the other instructors. The next year I decided to experiment, so I dressed more formally including a tie and everything. I was amazed that the students gave me far more respect simply based on how I dressed. To me how a person dresses has no effect toward their competence on the job, but now I realize that most other people don't see things that way. (Also my opinion of humanity went down a notch when I realized this, but again I digress...).
Anyway my take on her is that I think she dresses how she wants to dress regardless of being in a work environment. I doubt she realizes the effect it has on her job performance. Since she is in a PR role, I think it should be pretty easy to explain to her that she needs to look the part. In this case dress code is part of the job description. If she still doesn't get it, then explain that even intelligent scientists are still shallow and petty people who judge a person based on their appearance. Furthermore this is a business and you want to take their money from them, so she needs to dress professionally to do so.