Is avoiding an aunt who is characterized by many actions that violate Islamic law (such as abandoning prayer and fasting, backbiting, envy, not holding as forbidden what God has forbidden, and poor upbringing of children) considered to be the severing of kinship ties mentioned in the Hadith, and how can children be protected from her and the mother's anger be avoided in this situation?

If the maternal aunt is bad, you must maintain ties with her in a way that does not cause a break in relations or harm, while trying to reform her. If you despair, then it is permissible to abandon her with a "beautiful abandonment" if it deters her or protects you and your children from the harm of associating with her. Beautiful abandonment means ceasing interaction without harshness or harm. It is permissible if interaction brings about a deficiency in religion or harm to oneself or in worldly matters. Legitimate abandonment does not fall under the prohibited severing of ties. It is always permissible to abandon people of innovation and immorality. To avoid the mother's anger, explain the situation to her gently, be good to her, and pray for her.