Interesting question. What some people see as "Obligations" others see as "Opportunities." Teachers of children of missionaries are in fact missionaries themselves. Missionaries are volunteers working for the Lord and are called to perform some function that contributes to the Kingdom. I am not sure any of us are "obligated" to do something for the Lord. Rather, to seize "opportunities" when they arise. This does not mean, however, that you take on so much to do that your teaching, health, relationship with Christ suffers.
Teachers in boarding schools have many opportunities after school and on weekends since the students are there 24 hours a day, 7 days a week. There are dorm parents who share some opportunities to work with children with teachers and teachers do become involved in athletics, clubs, Bible study, counseling, etc.
Teachers in day schools may have of some of these same opportunities but since the students leave after school many of these possible opportunities end.