Is the work of a married woman as an elementary school teacher—with her commitment to the legal hijab, her non-mixing with men, and her lack of financial need for the work—considered unlawful or does it involve any suspicion of unlawfulness?

There is no harm for you in continuing this work as long as you adhere to good conduct and morals. A woman must observe hijab (definition) from an adolescent boy just as she observes it from an adult, due to Al-Nawawi's statement: "An adolescent is like an adult," and because an adolescent "can discern a woman's nakedness," meaning he is capable of describing what he sees of women. This is unlike a child who cannot discern a woman's nakedness, as stated in the verse: "Or children who are not yet aware of the private aspects of women."