How can one deal with a father who favors one of his children over others, hands over the reins of his business to a dishonest son who causes devastating financial losses to the family, and allows himself to deal with suspicious individuals despite the mother's warnings, knowing that the father rejects any advice and insists on his decision that "this is my money and I am free to do with it as I please"?

You must repent to Allah for bad words directed at others, such as backbiting (gheeba) and slander (buhtan), which are unbecoming of a Muslim. Severing ties of kinship is a grave sin, and abandoning prayer is even greater. It is not permissible for a father to favor some children over others unless there is a legitimate Sharia reason. If the father reaches a stage of interdiction, his case should be brought before the Sharia court to appoint a guardian over his wealth. Otherwise, his actions are valid, and the children cannot file a lawsuit against him except regarding favoritism if it is not based on evidence. You must honor your father, respect him, and maintain ties with him; his right is not diminished by his favoritism towards your brother, as mentioned.