What should a mother do when she intervenes to correct her wayward son, and the father sides with the son against her, causing the son to overstep his bounds with her and treat her as a stranger, and the father is pleased with that?

What the questioner mentioned is not among the ethics of a Muslim family raised upon the Book of Allah and the Sunnah of His Messenger, for it is obligatory upon the son to obey and honor his mother. It is forbidden for him to overstep her bounds or respond to her with any word that might hurt her, as Allah Almighty says: "So do not say to them [anything that indicates] disapproval and do not scold them but speak to them a noble word. And lower to them the wing of humility out of mercy and say, 'My Lord, have mercy upon them as they nurtured me when I was small.'" The father should advise his son and urge him to listen to his mother's counsel, and not condone his mistakes. The mother should be gentle in her advice to her son and obedient to her husband in what is good.