Am I right to reconcile with my aunt by offering her money and kind words through my wife without my mother's knowledge, given that my mother does not want me to reach out to my aunt, and I do not want to displease my mother?

Your action is correct in appeasing your mother and not obeying her in severing ties with your kin. However, you should gently advise your mother, explaining that severing ties of kinship is a major sin and that Islamic law commands maintaining kinship ties. You can seek the help of wise individuals to reconcile her with your aunt. In the interest of reconciliation, it is permissible to tell each of them words that foster affection, even if they are not entirely true, based on the Prophet Muhammad's (peace be upon him) saying: "He is not a liar who reconciles between people, saying good words and conveying good news."