How can one convince parents to remain in their homeland and abandon their life abroad after obtaining residency, especially given their prior refusal, citing self-reliance and building a future, and considering their current work in a mixed-gender environment?

It is not permissible for a woman to work in places where men and women intermix, especially in disbelieving lands, due to the unlawful conversations and private meetings that result from it. Furthermore, it is not permissible for a woman to travel without a mahram (unmarriageable kin) and reside in disbelieving lands unless absolutely necessary. Therefore, it is not permissible for you to return to those lands for mixed-gender work, and obedience to parents in this matter is not obligatory.