It depends on your child’s performance level. If he or she is a phenomenal talent, even some questionable grades wouldn’t disqualify him or her from places like Vanderbilt or Michigan, necessarily. On the other hand, if your child is not a phenomenal talent, you might consider that he or she should not major in violin performance in the first place, especially if there’s anything else in which he or she has interest and aptitude.
All that being said, The Cincinnati Conservatory at The University of Cincinnati offers scholarships and has an excellent strings faculty, including for violin. Stony Brook University (New York, but not in the city) does as well. University of Memphis also might be of interest to your family.