What is the ruling on a father's supplication against his son, while falsely accusing him, knowing that the son is wronged and has not fallen short in his duties towards his father?

A father's prayer against his child, when unjustly made, is not permissible and will not be answered. A child's disobedience (uquq) does not justify a father's injustice towards his son; rather, the son is still obligated to honor his father and treat him with kindness, even if the father acts wrongly.

As for the aunt's fabrication against the brother to avoid the father's anger, this is a grave error and a great sin, because it involves accusing a believer falsely. She must repent and inform the father of the truth, confessing her injustice towards your brother.