What is the ruling on abandoning a mother who does not pray, works in a shisha café, communicates with a foreign man, and sends him indecent pictures, after being advised and refusing to respond?

Your mother is in great peril by abandoning prayer and communicating with non-mahram men. The sin is even greater if she does this while married, due to her negligence of her husband's rights, for a righteous wife preserves her husband in his absence. Your father is accountable for her before Allah, as she is still under his responsibility. It is obligatory for you to advise her and your father gently and kindly, reminding them of Allah and His punishment. You must not abandon her, but rather you must honor her. If your father does not prevent her, then your brothers or her male relatives ( عصبتها ) must prevent her. If it necessitates confining her, they should confine her. She must be prevented from forbidden acts, even if by confining or restricting her. However, it is not permissible for a child to hit his mother or to cease honoring her, nor is it permissible to inflict a حد (prescribed punishment) upon her by killing or otherwise.