All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad, sallallaahu 'alayhi wa sallam, is His slave and Messenger.
If the aforementioned widow has no relatives other than those mentioned in the question, then her entire estate goes to her brother -whether he is a full brother (from both parents) or a paternal half-brother (from the father’s side only). Neither a brother’s son nor a sister’s son inherits with him (the deceased’s brother).
If, however, this widow’s brother passes away, then her estate moves to the sons of her brothers, because they are her ʿAṣabah (i.e. paternal relatives entitled to inherit what remains after other heirs get their fixed shares). In such a case, the estate will be divided equally among them.
However, this matter requires more detail regarding the brothers’ sons - whether they are sons of full brothers, or sons of paternal half-brothers, or whether their situations differ. For this reason, one should never rely on this general explanation alone when dividing the inheritance.
Allah knows best.