Am I sinful for the jealousy and hatred that developed in my brother's wife towards me, and her demand for divorce, knowing that I used to criticize her in front of my brother? And what must I do to repent?

You are not being unjust if you complain about your brother's wife without exceeding the bounds. If your criticism of her mistakes comes after warning her and she does not desist, and informing her husband is a way to prevent her from wrongdoing, then there is no harm in that, and it is not considered prohibited backbiting. However, mentioning her flaws, disparaging her, or mentioning her mistakes without a [valid] purpose is prohibited backbiting. Repentance for this involves ceasing the act, regretting it, and resolving not to return to it. Part of perfect repentance is seeking absolution from your brother's wife, or mentioning her favorably to those to whom you spoke ill of her. If seeking her absolution would lead to harm, then your repentance and speaking well of her suffice.