Will they be sinful if the quarrel and estrangement between the two brothers continue for more than three days, and they do not exchange greetings except by returning the general greeting to the household?

It is not permissible for a brother to insult his brother or harm him verbally or otherwise. He should be compassionate towards him and be like a father to him in kindness and respect. It is not permissible to abandon someone for more than three nights, and the better of them is the one who initiates the greeting. Abandonment ceases with merely greeting and returning the greeting, according to most scholars, while others believe it does not cease until they return to the state they were in before the abandonment. If refraining from speech harms him, then abandonment is not broken by a mere greeting. They must both end the abandonment in the way prescribed by Islamic law, and reconnect with each other.