I'm not a teacher but have done some teaching at university - it has the same sugar-lowering effect on me as exercise does! I always take a bit less insulin before I do it.
In terms of managing stress... it took me three years and a nervous breakdown to realise it, but diabetes occupies a reasonable fraction of your time, your head, your life. I was a very high achiever, but I had to give up my old expectations of myself. I had to allow more time for diabetes, allow more time for relaxation, be more forgiving of myself, put in more effort to enjoy life.
A key part of living with diabetes is educating those around you. Not everyone you see, but those who need to know. Your family, your employer, probably your students. Make sure your employer knows that a hypo is a medical emergency that needs immediate treatment. Make sure your family knows that diabetes is a largely invisible disease that is always there, taking little bites out of you, and their support is appreciated.
A big source of pain for me in the early days was that the doctors told me and my parents that hypos manifested with symptoms like "hunger, sweating, shaking", progressing to "confusion, dizziness". They didn't say that hypos could lead to horrible, confusing, terrifying emotions. Terror, anger, aggressiveness. (Maybe you'll have different reactions to a hypo, but the point is that life will be a lot better if you take the time to explain the important things to people.)