Do we, the children, sin by our silence about our mother's actions and what she did, and by not informing our father of what she was doing?

Disobeying the mother does not prevent showing her filial piety and kindness. Rather, she must be commanded to do good and forbidden from evil gently. Someone should have been brought in to deter her when she insisted on her wrongdoing, and claiming illness or insanity is of no avail. There is no sin upon you for not informing your father of your mother's actions due to his severity, as it was expected that the matter would worsen. Now that the mother has ceased her actions, praise Allah for that and forget the past, and turn to obedience to Allah, and adorn yourselves with good manners and character.