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.
The daughters of the brothers [i.e. nieces from the brother’s side] have no right to the inheritance because a daughter of a brother is not among the heirs. Similarly, all the sons and all the daughters of the sister [i.e. nephews and nieces from sister’s side] are not among the heirs. Besides, whoever dies before the death of this woman, whether he is her husband or her brother, or her sister, he does not inherit her. According to the consensus of the scholars a person who dies first does not inherit a person who dies last.
So, if the woman whom you mentioned in the question does not have an heir other than the three sons of her brother, and her brother was a full brother, or from the father’s side only, then all her inheritance will be for them as there are no other male heirs and it should be divided amongst them equally according to their number.
Moreover, it should be noted that the matter of inheritance is very complex an issue, so a mere Fatwa which is an answer issued according to the question is not enough. Rather, the matter should be taken to an Islamic court to look into the case, or it should be presented orally (in person) to the scholars in case there are no Islamic courts. It might be that there is an heir who would not be known except after investigation, and there might also be a will, debts, or other dues that are not known to the heirs. It is known that these rights come in priority over the right of the heirs. Therefore, the inheritance should not be divided without resorting to an Islamic court, if any, in order to fulfil the interests of the dead and the live people.
Allaah Knows best.