Is it permissible, Islamically, to sever ties with a brother and his children due to his repeated theft of his brother’s property, despite knowing that he is trying to reconcile, and would this severing of ties be considered a breaking of kinship ties that necessitates sin?

Maintaining kinship ties is obligatory, and severing them is forbidden. The one who maintains ties is not merely he who connects with those who connect with him, but rather he who connects with those who cut him off and shows kindness to those who mistreat him. We advise you to maintain ties with your brother and not to cut him off, even if he mistreats you. Regarding the money he took from you, if you are certain of it and have proof, you can mediate through someone who has influence over him to convince him to return the rights. If he refuses, then recall the words of Allah Almighty: (فَمَنْ عَفَا وَأَصْلَحَ فَأَجْرُهُ عَلَى اللَّهِ) "But whoever pardons and makes reconciliation – his reward is due from Allah," and His saying: (ادْفَعْ بِالَّتِي هِيَ أَحْسَنُ السَّيِّئَةَ) "Repel evil with that which is better." If you refuse, there is no harm in taking his matter to court to reclaim your right, though we do not prefer this due to the potential severance of kinship ties that may result.