All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
If what you mentioned in the question is confirmed that your brother behaved un-Islamically, like backbiting, causing the cutting of family relations and other misconduct towards your family, and you kicked him out of the house because of all of this, then you are not sinful, Allaah willing, for doing so. This act [kicking him out] by itself is not an act of disobedience to Allaah and it is not considered as severing kinship relations, which dispraised. Your parents should not have deserted you and left your home just because of this, if it is confirmed that they did so. It is also not permissible for your brothers to cut relations with you because of this.
Therefore, we advise you to be wise and try to solve this problem, as it is religiously required for relatives to be as loving and affectionate towards each other as possible, especially with the parents, because their right is great. No matter how kind and dutiful you were towards them, you would not have fulfilled their rights as you should, therefore, you should not remind others with your favours upon them or upon anyone else as this nullifies the reward of one's deeds.
For more benefit on being kind and dutiful to the parents, please refer to Fataawa 86620 and 84942.
You should also be careful not to mistreat your parents even when they mistreat you, because if you mistreat them you are severing relations with them. For more benefit on severing the relations with parents, please refer to Fataawa 84723.
You should earnestly supplicate Allaah to help you in reconciling with them, and you may seek the help of some pious and righteous people and those who may influence your parents and your brothers and sisters so that Allaah may reconcile between you.
As regards your statement "I got this reward for my full obedience to parents", we hope that you are not saying this as a way of boasting and reminding your parents with your favour upon them. You should know that Allaah tests people with whatever He wishes in order to test their hearts so that they would be patient -as patience is an act of worship- and so, He will wipe out their sins and raise their ranks.
For more benefit on the excellence of being patient when afflicted with calamities, please refer to Fataawa 88764 and 87510.
Allaah Knows best.