Praise be to Allah.
The father’s wife is a mahram to his sons and his sons’ sons, because Allaah says (interpretation of the meaning): “And marry not women whom your fathers married, except what has already passed; indeed it was shameful and most hateful, and an evil way” [al-Nisa’ 4:22].
With regard to the mother of the father’s wife, she is not a mahram to his sons, because there is nothing to indicate that this is the case. Allaah, may He be exalted, says after mentioning the women who are mahrams (interpretation of the meaning): “All others are lawful…” [al-Nisa’ 4:24].
The scholars of the Standing Committee for Issuing Fatwas were asked: My father has taken another wife besides my mother. Is the mother of this wife a mahram to my father’s sons from his other wife, or is she a non-mahram and is it haraam for them to meet her, sit with her and be alone with her?
They replied: The mother of the father's wife is regarded as a stranger (non-mahram) to his sons from another wife and his sons are not mahrams to the mother of the father’s wife. So she must observe hijab and it is not permissible for them to be alone with her or for her to travel with them, because they are not mahrams for her. End quote.
Fataawa al-Lajnah al-Daa’imah, 17/358
And Allaah knows best.