Is it permissible to sell the car registered in my name—which my brother owns—without his knowledge, and to use its proceeds to start a personal project, as a form of punishment for his attempts to assault my wife and sister, knowing that if he finds out what I have done, he will cut off our expenses?

What the questioner mentioned about his brother is a reprehensible evil, and he is obligated to protect his wife and sister and prevent his brother from what he intends. It is not permissible for him to sell his brother's car without his permission, as the sale is invalid according to Sharia (definition). He must provide for his wife and children equitably, and if he finds nothing, he must work and earn to support them. Muhammad ibn al-Hasan (definition) and al-Buhuti mentioned the obligation of earning for those who have dependents or whose maintenance is incumbent upon them, and that self-sufficiency and preserving one's dignity from need is better, in accordance with the Prophet's (PBUH) saying: "For one of you to go out early and gather firewood on his back and give charity from it and become independent of people is better for him than to ask a man who may or may not give him; for the upper hand is better than the lower hand, and begin with those whom you support."