Does she do better if you're not there, milkyway? Sometimes kids exhibit extreme neediness when their mother is there, but can manage to cope when mom isn't there. Does she regularly have these episodes if you aren't present?
strong will or anxiety -- your words
Anxiety. I doubt if your child is "refusing" to go certain places; it's just too difficult and "scary" for her. The standing in line with her was an excellent way for you to help her function at school and yet help to calm her fears.
I might suggest you google the phrase "children and anxiety" or "separation anxiety and children" or "anxiety and school" or similar words/phrases. There is a difference between separation anxiety disorder and separation anxiety (I suspect you daughter suffers from the latter which is not nearly as severe as the former). I expect she might need some help adjusting to school and you should be able to find some ideas from googling one or all of the above phrases. In addition, there are many books that can be purchased on-line or in a bookstore or borrowed from your public library on anxiety issues. One I might suggest is "Keys to Parenting Your Anxious Child" by Katharina Manassis. Patience, understanding and education of anxiety will go a long way in helping your daughter. I wish you the best ...