Mark, has some very good suggestions.
I must say as a retired elementary school principal that I never would have a child spending a lot of time in my office if they were 6. Behavioral modification starts by immediately and consistently taking action. Sending a child out of the classroom to the principal is not dealing with the problem. But, of course, I was not there to see what was going on. But, it does make me wonder how experienced the teacher is/was.
And ya, "The mother has taken her to counselors to no avail." What does that mean. The counselor must have made suggestions?
What your grand daughter requires are firm boundaries, limit setting, and discipline for her unruly behavior. Secondly, it is important for her to receive mental health counseling to help her cope with all the losses in her life which very well could be triggering the behaviors you described.
To be honest with you, I have no idea what this means:
"The mother has taken her to counselors to no avail."
Developing a meaningful rapport can be a challenge which takes time. Overnight change should not be expected. Depending on the severity of the emotional problems can determine the length of the counseling. Your grand daughter should receive individual, group, and family therapy. It would be ideal taking her to see a counselor that could provide all three forms of treatment. Additionally, the school counselor might be able to provide this treatment. Therapy is where meaningful change begins.