Is it permissible to imprison a parent, and what is the ruling on a son who filed a lawsuit against his mother after her vexatious lawsuits and threats of defamation? And are the children considered disobedient in this case?

The status of parents is great, and Allah has joined His right with their right, especially the mother, as her right is greater. Among the best ways to show filial piety to parents is to strive to improve the mother's situation by supplicating for her and seeking help from people of goodness. If the incitement of neighbors is proven, they should be confronted and advised, with a threat to escalate the matter to the competent authorities if necessary. It is not permissible to cause the mother to be imprisoned, as this contradicts accompanying them with kindness and good treatment, just as jurists prohibited imprisoning a father for his son's debt. The brother must be careful not to cause any harm to his mother, and he must repent and ask for her forgiveness if he has done so. Merely failing to improve the situation does not constitute disobedience. The mother's maintenance is obligatory upon her financially able children.