Does the mother of the husband have a right to the house inherited from her former husband? And does the wife have the right to demand separate and independent housing, especially in light of problems with the husband's mother?

If the wife's mother was divorced by her father, and her iddah (definition) (waiting period) ended before his death, she has no right to inherit from him. The wife's demand for a separate dwelling is her right, but it should be done with wisdom and consideration for the husband's circumstances and his mother's needs. Helping the husband to be dutiful and kind to his mother carries immense virtue and great reward, and Allah does not let the reward of those who do good go to waste.