One of the major problems affecting Muslims and non-Muslims in this country is the simple fact that the Muslim faith is far more intertwined into everyday life than the Christian faith. I entirely agree with respecting the dress codes of any faith. When my family went to Yogoslavia, we took a day trip to Venice, and ladies were advised in advance that arms and legs were to be covered if they wanted to enter the Catholic cathedral. Those who ignored the advice were not admited. As we know, the Catholic church in this country makes no stipulations about observances of visitors, but the Music faith does, and it should be respected. I attend Mass with my family regularly - as an atheist, should I not stand for hymns, kneel for prayers, offer the sign of peace or listen to the homily? None of it means anything at all to me, but the issue is respect for the people who do, in their place of worship. If your daugther attends a mosque, it is courtesy and respect to adhere to dress codes. The beliefs may not be your daughter's, but respect is universal, and you should lead by example.
I would check if your daughter is actually required to cover her face, which is not a Moslem edict, but a matter of choice for Muslim women - find out from the mosque in advance.
With regard to the teacher's aleged comments, have a word with the Head, and ask for an investigation.