Is my saying, "I will take my right on the Day of Resurrection" or "Peace is for Allah, not for you," considered a mistake or a sin after covenants have been broken and peace arrogantly rejected? And was it normal for me to retaliate in kind by slapping him after he strongly slapped and humiliated me in front of everyone? What is Islam's stance on a man who orders the cutting off of kinship ties, breaks covenants, insults people, and does not return greetings of peace?

Your statement, "I will take my right from you on the Day of Judgment," is not a sin. Your uncle's consideration of it as such is a false pretext for his anger at your demand for your right from him. It would have been more befitting for him to show leniency in settlement, as this falls under the Prophet's supplication: "May Allah have mercy on a servant who is lenient when he sells, lenient when he buys, lenient when he settles, and lenient when he demands settlement." Your good deed in not retaliating in kind and maintaining your connection with him carries a great reward, for the one who maintains ties is he who connects with those who cut him off. Your uncle's refusal to return the greeting and extend his hand in handshake is an injustice and a disgraceful act. It was obligatory for you to say to him: "Returning the greeting is obligatory," then turn away. Retaliating a slap in kind is permissible, but patience and forgiveness are more virtuous, especially from your uncle. "And the retribution for an evil deed is an evil deed like it, but whoever pardons and makes reconciliation – his reward is due from Allah." Returning a greeting is obligatory and a right for a Muslim. "And when you are greeted with a greeting, greet in return with one better than it, or [at least] return it [in a like manner]." It is impermissible to belittle or insult people, as this is a form of arrogance that prevents entry into Paradise. Your brother's act of reconciling between you is a great deed. "So, fear Allah and amend that which is between you." Continue to maintain ties with your uncle, treat him kindly, and be patient with his harm. "If you are as you say, then you are feeding them hot ashes, and you will always have a supporter from Allah against them as long as you remain in that state."