Is a Muslim female dentist sinful when examining men and mixing with male doctors, knowing that she is forced to uncover her palms in front of non-mahram men while working in a government hospital?

If a woman’s work necessitates unlawful mixing with men, or treating them without necessity, then it is not permissible for her to remain in it. As for her uncovering her hands such that men see them, there is no harm in it when there is a need, while taking precautions not to display them more than necessary.