Is it permissible for a brother to prevent his sister from cutting her hair, and would the sister be considered disobedient and wrong if she cuts her hair without her brother's knowledge and consent, especially if the mother is pleased with it?

Your brother has no right to prevent you from shortening your hair. It is permissible for a woman to cut her hair unless it involves imitating men, disbelievers, or immoral women. The forbidden imitation is that which pertains to disbelievers or men, and not every agreement is considered imitation. What your brother says about the obligation of you obeying him as a wife obeys her husband is unfounded. Rather, obedience to him is obligatory in matters concerning your protection and keeping you away from corruption and unlawful acts. Your brother has the right of kinship, so it is obligatory to maintain ties with him and forbidden to sever them. He, too, must maintain ties with you, and it is not permissible for him to shun you without just cause. If he is the one who severs ties, then you should maintain them to earn the reward for maintaining kinship.