A verse of the Holy Quran strongly emphasizes the importance of brotherhood and the closest of brotherhood should be first felt and started between siblings.
The Holy Quran says,
The believers are but brothers, so make reconciliation between your brothers and fear Allah that you may receive mercy.
Surat al-Hujurat 49:10
Sibling rivalry is sometimes apparent and other times hidden. Its so easy to solve this when it is hidden because when one is so connected with the other and comes from single parents, their hearts soften easily specially if they keep on trying. When this indifference gets more intense such that the actions towards one another get cold, then it could turn to a grudge or dislike but never can it be hatred.
We ought to remember and try our best to help our brothers and sisters, this way, we will begin to feel like helping our brothers and sisters in faith too. In reality we are helping ourselves. When we pray for them, the angels pray for us. Fulfilling the rights of brotherhood in Islam is a means for Allah to support us and reward us in the Hereafter. Failing our brothers and sisters in Islam results in Allah withdrawing this support.
Try to meet often and take gifts for your siblings to patch up. Write messages and congratulate them sincerely on happy occasions. Show warmth for them in your words and actions even if it be through sending messages or emails and better still by sending gifts for them even if they're small.
I guess if one party is ready to realize this and give in, slowly it will make a huge difference and the relationship amongst the siblings will become stronger with efforts and prayers for the betterment of themselves and the community.
If this is done exclusively for the sake of Allah, it will make things easier inshAllah.