Is it permissible to distance oneself from one's mother and live away from her to avoid continuous problems and her provocative curses, while being careful to visit her and show her kindness, when her nature is difficult and she frequently pronounces excommunication (takfir) and insults when angry?

Your mother's Islam does not vanish except with certainty. You are obligated to be dutiful and good to her, to supplicate for her guidance and repentance, and to advise her gently and kindly. You should also seek out someone who has influence with her to advise her. It is obligatory to detest the reprehensible acts she commits without falling into disobedience. If you have been disobedient, then you must repent and seek her forgiveness. There is no harm in living far from her if you feel safe and do not leave her to be lost, provided you visit her and maintain communication. You must frequently remember Allah, recite the Quran, and associate with righteous women to avoid the negative effects of your mother's actions.