Is the woman considered sinful if her brother refuses reconciliation after she initiated forgiveness, prayed for him, and sought reconciliation through their mother?

The Islamic Sharia encourages observing Islamic brotherhood, especially among relatives. If siblings oppress their kin, they are wrongdoers. If you are not the one who cut ties, then there is no sin upon you, and the sin falls upon the one who severed the ties. Pardoning them and your desire to maintain kinship are good deeds that bring you closer to Allah. If you were the one who cut ties, then forgiveness alone is not enough to end the estrangement; at the very least, greeting them is required. The best among those who are estranged is the one who initiates the greeting. If you do so and they do not respond, then you are absolved, and the sin is upon them. You should not despair but strive for reconciliation and supplicate to Allah.