The Prohibition of Marrying One’s Father’s Wife
Question: What is incumbent upon a man who has married his father’s wife, bearing in mind that she has children from him?

Answer: Allah, the Exalted, has forbidden marrying a woman whom one’s father has married. He says, “And do not marry those women whom your fathers married, except for what has already passed. Indeed, that was an outrageous act, hateful to Allah, and an evil way.” [al-Nisa 4:22]

Whoever regards such a union as lawful has fallen into disbelief and has apostatized from Islam. If, however, he entered into the marriage out of ignorance and did not consider it permissible, he has committed a grave error. The contract is void, they must be separated immediately, and he should be strongly reprimanded for it.
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The Wife’s Mother Is a Mahram
Question: Is it permissible to shake hands with one’s mother-in-law and to travel with her? Please advise us—may Allah bless you.

Answer: Yes, there is no harm, because she is one of your unmarriageable relatives (mahram). Allah, Glorified and Exalted, has made the wife’s mother permanently forbidden to her daughter’s husband; therefore, she is your mahram. You may shake her hand, travel with her, and act as her mahram—unless you fear temptation. If there is any risk of fitnah, then you should not shake her hand. But if no such concern exists, it is permissible to shake her hand, to accompany her on a journey, and to serve as her mahram, for she became permanently forbidden to you by virtue of your marriage contract with her daughter. And Allah knows best.