What should a son do if his divorced mother — who is still married to another man — and his father are living in the same house, and then the mother starts stirring up trouble between the children and the incapacitated father? Should he ask her to leave and go live in her husband’s house?

It is not clear whether the mother is staying with her children and has left her husband's house. If it is with his consent and there is no seclusion with the father (of the children) or temptation (fitna), then there is no objection. Otherwise, it is not permissible. She should be advised gently if she is causing problems, while continuing to treat her kindly and with beneficence.