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, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
The question is rather unclear. We can briefly say that the deceased's nieces (daughters of the deceased's brother) have no share in the estate of their paternal aunt because the brother's daughter is not among the rightful heirs to begin with. The same applies to the brother's wife; she does not inherit from her husband's sister or brother.
As for the son of the deceased's full brother or half-brother on the father's side, he is among the heirs of his paternal aunt. However, he is excluded from the inheritance in this case given the presence of the deceased's direct brother (the brother of his paternal aunt, i.e. his paternal uncle). In other words, the son of the deceased's full brother does not inherit from his paternal aunt in the presence of his paternal uncle (her direct brother) regardless of whether her brother was living with her or not and whether he maintained relations with her or not. He is among her heirs in all situations as long as there are no other 'Aasib (male relative on the father’s side), because the reason for the entitlement to the inheritance is the blood relationship, and not the upholding of the ties of kinship.
As for your question whether you are entitled to inherit your father's share in your paternal aunt's estate, you should know that if your father passed away before the death of your paternal aunt, he is not entitled to any share in her estate. The one who died first does not inherit from the one who died after him. However, if your father passed away after the death of his sister, then he has a share in her estate, and this share passes to his own heirs upon his death.
If the deceased left behind one full brother and one full sister only, the estate should be divided among them by virtue of Ta‘seeb (having a paternal relation with the deceased and not having an allotted share, so they get what is left after the allotted shares have been distributed); the male gets double the share of the female. Allah, The Exalted, says (what means): {…if there are brothers and sisters, the male will have twice the share of the female.} [Quran 4:176] Hence, the estate should be divided into three shares; the brother (your uncle) gets two shares, and the sister (your aunt) gets one share.
Lastly, you said, “My dead aunt nominated my surviving aunt in her shares.” If you mean that she made a will in favor of her sister to take this share, then you should know that it is forbidden to make a will to an heir, and it cannot be executed except with the consent of all the other heirs. Hence, your living paternal aunt is entitled only to her share in the estate.
Allah knows best.