Is emigration obligatory for the sake of the religion of the spouses and children, and what is the solution if it becomes difficult, given that the spouses work in a mixed educational environment?

In your situation, emigration is obligatory if you do not feel secure about yourself or your family regarding religious temptation (fitna), and you are unable to practice the rituals of your faith, provided you are capable of emigrating. If you are unable, then Allah does not burden a soul beyond its capacity. In that case, you must fear Allah as much as you can, strive to lower your gaze from forbidden sights, and avoid mixing with non-mahram (definition) women. Your wife must also be careful to avoid mixing with non-mahram men, adhere to the hijab (definition), and avoid seclusion if she needs to work.

Scholars have differed on the ruling regarding emigration from countries where sins are committed: The Malikis: They consider emigration obligatory from a land where sins are practiced. The Shafi'is: They consider emigration obligatory for anyone whose truth is not accepted or who fears temptation (fitna) therein, because remaining and witnessing evil is itself an evil. The Hanbalis: They believe that emigration is not obligatory from among people who commit sins. Mulla Ali al-Qari: He believes that emigration from a homeland where good is abandoned and evil spreads is commendable (mandub).