Is a mother's prayer always answered, and does a mother's cursing and threatening her daughter for her commitment to religion affect the acceptance of her acts of worship?

Your mother is in great danger, and she is unjust and abusive towards you, yet she has a right over you. Associate with her with kindness, obey her in what is good, adhere firmly to your religion, remain steadfast in truth, seek help from Allah, and supplicate frequently. If you fulfill what is due to her, her supplication against you will not harm you, for a parent's supplication against their child is effective only if the child has wronged them. Rejoice in great goodness and immense reward, for Allah does not let the reward of those who do good deeds be lost.