How can one deal with a cruel and unjust mother who constantly curses her daughters and mistreats them?

What you have mentioned about your mother's mistreatment is heartbreaking. However, for a believer, the mercy of Allah suffices beyond all people, and calamities are expiations and elevations for believers. Your mother's ill-treatment does not negate her right to your dutifulness and kindness. The best way to repel her ill-treatment is by being kind to her, for kindness can turn an enemy into a friend, as Allah Almighty says: (And not equal are the good deed and the bad. Repel [evil] with that which is better; then suddenly that between whom and you was enmity will become as though he was a devoted friend.)

As for your mother's supplications against you without just cause, this is not permissible, and such a supplication is rejected and unanswered, as stated in the Hadith: "The supplication of a servant continues to be answered as long as he does not pray for a sin or cutting off ties of kinship." Therefore, your mother's supplications against you without just cause will not harm you.

There is no harm for you in moving to a separate residence from your mother to avoid her harm, provided there is security from temptation and avoidance of suspicion and ill thoughts about you. This is unless the mother is harmed by such a move.

Your statement: "And the supplication that shakes the Throne of the Most Merciful" should not be uttered, as such an expression lacks evidence.