What is incumbent upon me after insulting someone older than me and verbally and physically assaulting them, knowing that they were the ones who initiated the assault?

A Muslim should respond to evil with good, as Allah Almighty says: "And not equal are the good deed and the bad. Repel [evil] with that which is better, and thereupon the one whom between you and him is enmity [will become] as though he was a devoted friend." You must repent for shaming the woman by resolving not to return to such behavior, regretting what you have neglected, apologizing to the woman and her daughter, and seeking their forgiveness. Do not despair of Allah's mercy, and increase in righteous deeds.