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 estate should be divided among all his eligible heirs who outlived him. Those who died before his death have no share in his estate. Hence, the deceased’s estate should be divided among his wife and children - sons and daughters - including those who passed away after his death. The deceased’s grandchildren and his children’s spouses have no direct shares in his estate. However, they are entitled to their due shares of his children’s estates, i.e. their immediate parents and spouses, who inherited from the deceased.
According to the information in your question, the deceased left behind a wife, five sons, and three daughters; two sons (the elder and youngest) and a daughter (youngest) passed away after his death. If the deceased has not left behind any other eligible heirs other than these ones, then the estate should be divided among his wife, five sons, and three daughters as per the sharee'ah. The sons’ sons and daughters are excluded by the presence of the deceased’s immediate descendants (children).
If the deceased has no other eligible heirs other than those mentioned in the question, then the deceased’s wife is entitled to one-eighth of the estate as a fixed share. Allaah, The Exalted, says (what means): {...But if you leave a child, then for them (i.e. the wives) is an eighth of what you leave...} [Quran 4:12]
The remainder of the estate, after deducting the wife’s share, should be divided among the deceased’s children by virtue of taʻseeb (i.e. by virtue of 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. Allaah, The Exalted, says (what means): {Allaah instructs you concerning your children (i.e. their portions of inheritance): for the male, what is equal to the share of two females...} [Quran 4:11]
The estate should be divided into 104 shares; the wife gets one-eighth (13 shares), and the children get 91 shares, each son gets 14 shares and each daughter gets 7 shares.
The shares of the deceased’s children who passed away after his death, i.e. the elder son, youngest son, and youngest daughter, should be divided among their eligible heirs along with their other properties. The elder son’s wife is entitled to one-fourth of her husband’s estate as a fixed share because he has no descendants, and the remainder of the estate is to be divided among his other eligible heirs: his mother and siblings.
The youngest son’s wife is not entitled to inherit from her husband because she passed away before him. Hence, his estate should be divided among his other heirs, i.e. his mother and siblings.
As for the youngest daughter, who passed away after her father’s death leaving behind a husband and two children, her estate, including her share in her father’s estate, should be divided among her eligible heirs: her husband, children, and her mother.
The above answers your questions, "Does the husband get a share, and do the two kids get a share from the property?" and "Do the grandsons and granddaughters get a share from the paternal grandfather’s property? Or do only their fathers get the share from their grandfather's property?" This also addressed your concerns as to whether the granddaughters (daughter's daughters) have a share of the grandfather's estate.
Allaah knows best.