Is a wife Islamically entitled to live in a separate house from her husband's family under the aforementioned circumstances, and will the husband be punished if his mother becomes angry with this decision?

An independent dwelling is a right for the wife, and the husband must provide it, especially if staying with his family causes harm. There is no blame on him for separating from them, even if they become angry, provided he attempts to convince them. The wife's salary is her property, and she can dispose of it as she wishes. Her husband has no right to prevent her from using it to maintain ties with her family. She is not obligated to help him with household expenses unless it was stipulated as a condition for him allowing her to work, although helping him with her money is commendable if he is in need. The husband's father, who does not pray and does not read the Quran, should be advised gently and wisely, to explain the seriousness of his actions.