Should a wife resign from her job, which she views as involving mingling and falling short in the rights of her home, husband, and daughter, despite her parents' strong opposition to her decision, to the extent that her father would consider her deceased if she did, or should she continue working to appease her parents, and would resigning be considered an act of disobedience to parents?

If there is unlawful mixing (of sexes) in a woman's work and study, then her abandoning them and devoting herself to raising her daughter, taking care of her home, and making her husband happy, is not an act of disobedience to her parents. She is not obliged to obey them in this matter, for there is no obedience to a creature in defiance of the Creator. She should apologize to her parents gently and kindly, explain to them the impermissibility of mixed-gender work and the lack of necessity for it, and seek mediation from someone who holds influence with them to persuade them.