I think that given we only have weather like this for maybe 10-20 school days a year, it wouldnt be too much to ask that children be allowed or even encouraged to protect themselves from the sun.
Mine are okay with all-day cream and although they still have a little bit of clolour I think it stops the worst of it - but one of their friends has very sensitive skin and has had no end of trouble.
It is bizarre that some schools are keeping children indoors whilst others are adopting a dont care attitude.
OP - do you have a friendly GP or practice nurse - could you get an "official" letter concerning the allergies to all-day suncreams and requesting that your DD be allowed to reapply the cream to which she is not allergic. Get copies, take it to the headteacher and the teacher and ask that it is kept on file for future years at that school. I think they have to take more notice then.