Not knowing the rest of the population that applies for the program, I would say that your daughter's application will look really good. In terms of writing an essay under supervision, just remind her to read the entire set of directions before she writes anything and make sure that what she writes answers the question. I would think they will be looking more for general writing abilities than specific techniques. I'm sorry I can't give you any more advice than that - being a physics teacher, I am definitely not the person you want to ask about writing an essay for an English teacher
(I am not a good writer, and don't really know much about helping kids write well.)
Good luck with the application!
