Is the questioner considered to be failing in her duty towards her husband, and was what she did for his sake and for the sake of her children wrong, and should she have separated from him when her father requested that, especially given her suffering from continuous hardships and debts, and her feeling of depression and loss of desire for everything, despite her belief in divine decree and destiny?

The cause of the depression you feel is a weakness in faith regarding divine decree and destiny. Despair does not enter the heart of a believer, for he recites Allah’s saying: "Allah will bring about ease after hardship" (Quran 65:7) and His saying: "For indeed, with hardship [will be] ease. Indeed, with hardship [will be] ease" (Quran 94:5-6). No punishment descends except due to a sin, and none is lifted except through repentance. Therefore, divorce should not be sought from the husband because of his debts unless he becomes unable to provide maintenance, in which case you may seek divorce due to harm.