How can one deal with a mother who exhibits nervousness in her interactions and speech, while desiring to please her and avoid mutual anger?

The mother's right is great, and disobeying her is one of the greatest sins. Therefore, it is impermissible to mistreat her or speak harshly to her. What is obligatory is to repent for what happened by angering her and to be keen on addressing her with politeness, gentleness, humility, and reverence. Allah the Almighty says: "So do not say to them [anything that indicates] disapproval and do not scold them but speak to them a noble word. And lower to them the wing of humility out of mercy and say, 'My Lord, have mercy upon them as they brought me up [when I was] small.'" One must strive against oneself to avoid anger, for anger is the root of all evil. Good manners are acquired through habituation and practice. The Prophet, peace and blessings be upon him, said: "Do not get angry." It is also advisable to frequently remember Allah and supplicate to Him.