After that, if busy work continued, I'd be tempted to suggest to her that she make her own judgement of which pieces of work are worthwhile and do only those, but I know it's hard. Does the history syllabus come with learning objectives? If so, a handy sentence to write some time might be "I decided not to do this as I didn't understand how it would support me in achieving any of the learning objectives of this course."
Of course, if she does that, the teacher may give her a poor grade, and this will at least slightly reduce her change of getting into a "good" college. How much time a teen should spend playing the college admissions game vs. actually getting an education is an interesting question.
If the mother complains to the administration, either on her own or together with other parents, about poor teaching, she may be branded as a troublemaker, and her daughter may get poor college recommendations from teachers. One needs to know the mindset of the teachers and administrators to judge the severity of this risk.
