Is it obligatory to work a second job after a government job until late at night for a similar income, despite its negative impact on one's health, life, and relationship with Allah, or is it sufficient to rely on the morning job?

If your official work covers your expenses and the expenses of those you support, do not accept additional work that affects your health or distances you from your religion. Advise your family with the hadith (definition): "Indeed, the Holy Spirit inspired in my soul that no soul will die until it completes its provision and its term, so fear Allah and be graceful in seeking."

However, if your salary is not sufficient, then seek another suitable job to achieve sufficiency, and you will be rewarded for that.