What is the jurisprudential ruling on dealing with a mother who speaks for long hours on the phone with a strange man (not a mahram), and what is your advice to me?

It is not permissible to abandon one's mother or to be insolent towards her. Rather, she must be advised and reminded with wisdom and good counsel, without argumentation or raising one's voice. One must repent to Allah and seek her forgiveness, and advise her with a gentle approach and soft words.