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It's well established that Fëanor hated Fingolfin, and had some dismay for Finarfin, aside from the fact he wanted a strand of his daughter Galadriel's hair.
Did Fingolfin hold a grudge against Fëanor's children too?
As in not care about his nephews because of the actions of their father towards him?
The hatred came from the lies of Melkor, telling Fëanor that Fingolfin wanted to become leader in place of Finwë & telling Fingolfin and Finarfin that Fëanor wanted them exiled.
This boiled over with Fëanor drawing his sword on Fingolfin
Fingolfin bowed before Finwë, and without word or glance to Fëanor he went from the chamber. But Fëanor followed him, and at the door of the king’s house he stayed him; and the point of his bright sword he set against Fingolfin’s breast. “See half-brother!” he said. “This is sharper than thy tongue. Try but once more to usurp my place and the love of my father, and maybe it will rid the Noldor of one who seeks to be the master of thralls.
The Silmarillion, Of the Silmarils and the Unrest of the Noldor
Fëanor was banished for 12 years for this act, even though Fingolfin immediately forgave his half brother. Once the 12 years were up Fingolfin again forgave Fëanor.
Then Fëanor took his hand in silence; but Fingolfin said: “Half-brother in blood, full brother in heart will I be. Thou shalt lead and I will follow. May no new grief divide us.” “I hear thee,” said Fëanor. “So be it
The Silmarillion, Of the Silmarils and the Unrest of the Noldor
Thereby tying Fingolfin's house into the fate of the house of Fëanor and of the Silmarils.
So despite all the ills Fëanor did to Fingolfin, Fingolfin wanted nothing more than to forgive and heal their brotherly bond. It would seem strange then that Fingolfin would hate Fëanor's sons for their father's actions when he is willing to forgive their father.
Following the Flight of the Noldor, the burning of the ships and Fingolfin's host having to cross the Helcaraxe there was no way for any further reconciliation to take place as Fëanor was killed.
However following Maedhros' rescue by Fingon, Fingolfin became King and the healing of the Noldor began. Fingolfin cemented this 20 years later at Mereth Aderthad the Feast of Reuniting.
The Mereth Aderthad ("Feast of Reuniting") was the great celebratory feast held at the order of High King Fingolfin in the twentieth year after the first rising of the Sun. The feast was held by the Pools of Ivrin, under the Mountains of Shadow to the north of Beleriand. Its purpose was to unite all of the divided Elves in one cause, and ambassadors came from all the peoples and realms of Beleriand. As well as Elves from the separate branches of the Noldor, native Grey-elves were also present, including some from Doriath and the Falas. Ambassadors even came from the Green-elves, the people of distant Ossiriand in the east
The Silmarillion, Quenta Silmarillion: Of the Return of the Noldor
So all through the books no grudges are shown to be held by Fingolfin only an immense desire to heal the rift that had grown between the sons of Finwë.
Fingolfin may well have held a grudge against his nephews, but not because they were Fëanor's sons — because of their parts in the burning of the ships of the Teleri on the shores of Middle-earth, and consigning so many of Fingolfin's followers to an icy death on their own journey to Middle-earth.
Fingolfin did forgive Fëanor for his misdeeds in Valinor, those were mere personal slights, and no real harm came of them. But the theft of the swan-ships caused the deaths of thousands of Fingolfin's followers, including his own daughter-in-law.
No love was there in the hearts of those that followed Fingolfin for the House of Fëanor, for the agony of those that endured the crossing of the Ice had been great, and Fingolfin held the sons the accomplices of their father.
-- "Of the Return of the Noldor" Quenta Silmarillion (The Silmarillion)
While Fingolfin ruled as a wise King, and he worked with Maedhros to heal the rifts between the two camps of the Noldor — knowing that standing divided would only make it easier for Morgoth to destroy them all — I do not know of any primary source that states how he personally felt about the Sons of Fëanor.
