Is it permissible for a brother to deprive his brother of the money he entrusted him with, claiming family disputes, and is refraining from communicating with him considered a severance of kinship ties after he has been psychologically and financially harmed by this act?

The nature of the transaction with the brother is not clear. If the price was a loan, then interest on it is impermissible and should be deducted from the amount. If it was a Mudarabah (profit-sharing partnership), then your specified share of the profit is permissible. It is forbidden for the brother to deny your right or to procrastinate in fulfilling it, as this constitutes consuming people's wealth unjustly, according to the Almighty's saying: "Do not consume your wealth among yourselves unjustly," and the Prophet's (peace be upon him) saying: "The wealth of a person is not lawful except with his willing consent," and his saying: "Every Muslim's blood, wealth, and honor are sacred to another Muslim." If your brother has a debt due from you and you refuse to pay it, he has the right to take his due without any increase (referred to as al-Zafar, taking one's right). Kinship ties should not be severed due to disputes, for the one who maintains ties is not the one who merely reciprocates, and it is better to maintain kinship ties despite his actions. Reconciliation is advised to resolve the dispute. A debt is repaid with its like, without considering changes in prices.