Is it permissible for divorced parents, who divorced by mutual consent, to remain in the same house with their children, knowing that the mother has reached menopause, they do not speak to each other, and there is no discord?

You should advise your parents against divorce, as reconciliation is better. However, if divorce occurs, it is not permissible for your parents to live in the same house after it, because their seclusion (khalwa) together would be forbidden. A woman is a source of temptation and desire, even if she is old.

If the mother is to live there, she must reside in a separate room with its own private entrance and exit, along with separate facilities (bathroom, kitchen, etc.); otherwise, it is not permissible for them to live together.