Is the mother of the brother's wife considered a mahram? And is this a permanent or temporary prohibition (for marriage)?

The mother of the brother's wife is not considered a mahram. Surah An-Nisa (Chapter 4) explicitly outlines the women who are mahram in verses 23-24, and the mother of the brother's wife is not mentioned among them. Furthermore, her prohibition has not been stated in the Sunnah or in the sayings of the scholars.