All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
If what you mentioned about your father is true that he is very cruel to your mother and your brother, and that he utters such obscene words about your mother and her parents, then he is indeed very wrong and unjust. In any case, you have to be kind and dutiful to him as the right of the father upon his children in being kind and dutiful to him is not dropped under any circumstances.
The best manner of being kind and dutiful to your father is to advise him kindly and gently, and endeavor to rectify him while supplicating Allaah and seeking His Help for his guidance. For more benefit, please refer to Fataawa 87019, 89302 and 88120.
If he is not deterred from such evil conduct, and it is hoped that deserting him would be beneficial, then it is permissible to desert him and this is not considered as being undutiful to him. Shaykh Ibn ‘Uthaymeen issued a Fatwa that it is permissible to desert the parents for a religious benefit while keeping ties with them through fulfilling their obligatory rights like spending on them and providing medical treatment for them among their other needs.
As regards hating your father because of his actions, then if this does not exceed this extent to reach the apparent actions that are not permissible to do with him, then you are not sinful and this is not considered as being undutiful to him. This is because the actions of the heart are something a person has no control over. Ibn Habeeb said: “Since the heart is something a person has no control over, and a person cannot be just in regard to the actions of the heart, Allaah does not hold a person accountable for it. Allaah Says (what means): {Allaah does not charge a soul except [with that within] its capacity.}[Quran 2:286]”
As regards mistreating your mother as you mentioned because of hating her, then you are sinful and you are obliged to repent from that. The fact that it is what your father says about your mother or that she is mistreating you that made you hate her does not exempt you from sin.
Also, it is not permissible to insult the family of your father, especially his parents, who are your grandparents. Rather, you should be careful not to insult in general, as the Prophet said: "Indeed the believer is not a slanderer, one who curses frequently, one who indulges in obscenity, or one who engages in bad talk." [Ahmad]
Moreover, if what you mentioned about your father is correct that he caused the dissension between you and your uncles and that he incites your younger brother to mistreat you, then he is sinful for this also.
As regards him favoring your youngest brother over you, then you did not mention to us for what reason. However, it is an established fact among the scholars that the parents should be just between their children in everything, so that this would help them in being kind and dutiful to their parents and prevent them from severing ties with them.
At-Tirmithi said after quoting the Hadeeth implying being just between one’s children: “Acting according to this Hadeeth, some scholars are of the view that being just between one’s children is desirable; some of them are even of the view that the father should be just between them even in regard to kissing them.”
Concerning favoring a child over others in gifting him, then this is not permissible unless there is a Sharee’ah-based reason.
With regard to the work of the son with his father in trade, then it can be either as a partner or a hired person or working for him voluntarily for no money. What determines one of these possibilities is the contract. If there is no contract between you and your father, then you should refer to the customs.
Anyway, it is permissible for the father to include one of his children as a partner with him in his business and give him part of the profit in return for his work and effort and in return for any capital money that he might have contributed in the business. In addition, it is more appropriate for him to include all his children if he can do so provided they are suitable for the business that he does.
Allaah Knows best.