Which is better: to work as a doctor while adhering to the rules of mixing, or to quit work and devote oneself to worship at home, especially in a country that needs doctors?

There is no objection to a woman working in a mixed environment with men out of necessity, provided she adheres to Islamic manners in her interactions with them, such as wearing the hijab, avoiding khalwa (private seclusion), and refraining from shaking hands. Her speech with them should be limited to what is necessary, while she strives to find work in a female-only environment if possible.