What is the ruling on supporting the mother in the event of the father's injustice, such as his marriage to an unsound woman?

You must treat your parents with kindness and associate with them in a good manner. If what you mean by the father's injustice to the mother is his attempt to marry another, then this is permissible for him. You should advise him to choose a woman of good character and religious devotion. The Messenger of Allah, peace and blessings be upon him, emphasized the mother's right more, but it is not permissible to obey the mother in what leads to mistreating the father, because there is no obedience to a creature in disobedience to the Creator. You must reconcile between them.