Have I lost my faith after cursing Allah -Almighty and Exalted be He- in a moment of anger and despair, and what should I do with my family and husband who do not leave me alone and treat me harshly?

If you cursed the Lord of Glory and Majesty, knowing what you were saying, then this is apostasy and disbelief that necessitates immediate repentance and return to Islam. And Allah may make the sin from which one repents a cause for His servant's mercy and entry into Paradise. As for your family members who are negligent in prayer and who seek to stir up discord between you and your husband, you should try to understand the reason for their actions and address what can be remedied. As for your husband, if he is mistreating you and beating you beyond the limits of Islamic law, he should strive for understanding instead of incitement. You should be patient and manage your husband, avoid everything that your family can exploit to turn him against you, and make abundant supplications. Divorce may not be in your best interest, especially given your family's distance from religion and their eagerness to harm you.