How can one repent and improve their relationship with their mother after raising their voice at her and making her angry? And does Allah forgive sins merely by asking for her forgiveness and pardon and her being pleased, even if the mother had cursed her son before forgiving him?

If you know that you are quick to anger, you must restrain your tongue and beware of anger and its causes, because a word that a servant does not discern may cause him to fall into Hellfire further than the distance between the East and the West. The Prophet, peace and blessings be upon him, warned against anger and repeatedly advised, "Do not get angry."

Raising one's voice at one's mother is an act of disobedience (uquq), especially when angry, as you might utter a word in anger that displeases Allah, without giving it any thought, and it could be the cause of your destruction. Allah Almighty said: {So do not say to them, "Uff," and do not repel them but speak to them a noble word.}

You must hasten to sincere repentance to Allah. And the mother should beware of supplicating against her child, because the supplication of parents is answered. If the son repents and his mother forgives him, then repentance erases what came before it.