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 deceased's niece has no rightful share in the inheritance because she is not among the eligible heirs. However, the deceased's nephew, either the son of the deceased's full brother or of his half-brother from the father's side is among the eligible heirs entitled to a share in the estate. The son of the deceased's half-brother from the mother's side is not among the eligible heirs.
If you are the sons of the deceased's full brother or half-brother from the father's side, you should have provided your number under the category of the male heirs entitled to the inheritance.
Generally speaking, the deceased's wife is entitled to one-fourth of the estate as a fixed share if the deceased has no offspring entitled to a share in the inheritance. She has no right to dispose of the rest of the estate other than her one-fourth because it is the right of the other heirs.
If there are no other rightful heirs in this category, then the rest of the estate goes to the blood relatives of the deceased. In both cases, the deceased's wife is not entitled to dispose of the rest of the estate either by offering it as a gift or in any other way.
Finally, we advise you to refer your case to a Sharee'ah court or knowledgeable scholars to identify the shares of the other eligible heirs or the blood relatives.
Allaah Knows best.