Is it permissible to abandon one's family due to their lack of religious commitment and their commission of major sins, and out of fear of being influenced by them? And is it permissible to marry without their knowledge for the sake of migration and to ward off corruption?

It is not permissible to obey one's parents in abandoning obligatory religious duties or committing forbidden acts. One must advise them with wisdom and explain the danger of abandoning prayer, while still being kind to them and supplicating for them. If your continued presence with them harms your religious commitment, then it is permissible for you to distance yourself from them. There is no impediment to marrying without their knowledge as a means of emigration, provided that the marriage fulfills its pillars and conditions, while continuously maintaining dutifulness towards them.