Too stressed to do your job is too stressed to physically be at work. This is just an excuse and not even a good one. I have personally seen people successfully work when grieving a spouses death, when getting a divorce, when dealing with a serious illness in their immediate family, when dealing with a serious illnes of their own. If you can't work, there is no excuse for allowing this to continue. This person needs to be confronted with her poor performance and immediately placed on some sort of emergency leave to get her life together or be fired.
I would suggest documenting the things she does that should not be happening during work hours such as the ebay surfing. I would document the tasks that are her repsonsibility that she has assigned to you. Document when she is late or takes too long a lunch or behaves unprofessionally in front of the students.
Once you have facts and fuguresfigures, set a meeting with all the other aides and the director and show him the documentation and ask that this person be put on leave or fired.