Your daughter has a right to sleep in her own bed. The way to refuse the request is to say “sorry, that doesn’t work for me.” If the roommate persists in asking, it’s not your daughter who’s damaging the relationship.
I wouldn’t be eager to have my daughter sleep out in the open in a dorm lounge. I wouldn’t feel safe sleeping out in the open like that and I wouldn’t want my daughter to do it either. And she shouldn’t have to sleep on someone’s floor either.