I think if your daughter wants to study in Morocco for a semester, she will enjoy every minute and the Moroccan hospitality will welcome her with open arms. I am an American woman who has visited Rabat and has experienced the kindness of the Moroccan people firsthand. Rabat is an exotic, yet very cosmopolitan capital city. Currently, my fiance is studying at the Universite Mohamed V in Rabat. The program there is rigid and intensive by all accounts. I know that the university in Iframe mentioned in earlier posts, although not located in a large city, hosts many international students and has Americans serving on its faculty.
As far as your daughter's freedom is concerned, I wouldn't worry too much about it. Many Americans(I can only speak about Peace Corps) have lived with host families for months, some in of them in their 50's. None of which have ever complained that they felt their freedom was restricted. In fact, I would think your daughter would be safer in a Moroccan family that will always look out for her best interests and make sure she has a warm meal everynight. I envy the opportunity she is afforded now, as I would have never considered visiting Morocco when I was that age. It just never occurred to me.
And if you have the time to visit her, please do. My fiance and I plan to spend our honeymoon in Marrakech and Essaouira, two diverse cities that are rich in Moroccan history and culture and are a must see for any visitor. If I can recommend a book to you about Morocco, check out former Peace Corps volunteer Orin Hargraves "Culture Shock Morocco". It introduces the customs and etiquettes of Morocco, as well as giving the "outsider" an up close and personal view of life in Morocco and how to live there.
All the Best,
Chris