Is it considered disobedience to not help one's father with carrying things, to tell him "I only love my brother" with the intention of provoking him, and to supplicate against him due to the severity of his treatment? If so, what should the son do, what is the formula for seeking forgiveness (Istighfar), and should it be with the intention for the deceased father?

The right of a father is great, and honoring him is among the greatest causes of Allah's pleasure, while disobedience to him is among the greatest major sins. His right to dutifulness does not diminish, no matter his condition or his wrongdoing. If you have caused your father annoyance or mistreated him, you have committed something forbidden, and this is a major sin of disobedience. Sincere repentance erases the effect of a sin, no matter how great it may be. It consists of abandoning the sin, regretting it, and resolving not to return to it. You can seek forgiveness for your father by supplicating for his forgiveness and mercy, and by making up for any shortcomings in your dutifulness to him by giving charity on his behalf, maintaining ties of kinship through his side, and honoring his friends.