Is it permissible for a divorced woman with three children, whose father does not provide for them, and who works in a customer service job at a telecommunications company where there is no mixing of genders, while her own father is elderly and has a low income, to continue in her job due to the lack of a better alternative?

It is permissible for a woman to go out to work in a permissible field if she adheres to the Sharia (definition) guidelines, including: maintaining Islamic dress, not using perfume or adornment, and avoiding mixing with men and being alone with them except out of necessity. If these conditions are met, then there is no objection to her working.