What is the Sharia ruling regarding someone who defended his mother from his father's abuse and beating, and then, in a moment of anger and anguish, hit him and yelled at him, and is now deeply remorseful?

The rights of parents are immense, even if they are disbelievers, as stated in the Almighty's verse: (But if they endeavor to make you associate with Me that of which you have no knowledge, do not obey them, but accompany them in [this] world with appropriate kindness).

What is required of the son when the father is angry is to control himself and remember Allah, and to try to calm the father wisely, and to prevent harm from reaching the mother.

As for the path to repentance from this sin, it includes: 1. Sincere repentance and remorse for what has passed, and a firm resolve not to return to such an act. 2. Seeking forgiveness and pardon from the father, and showing kindness to him by every possible means. 3. Not despairing of Allah's mercy, for Allah forgives all sins for whoever repents, believes, and does righteous deeds.