Once you get accepted in the Children of Atom cult and with the quest “What Atom Requires” is active, talk to Richter to start this quest. (Longfellow will dislike this quest). Talk to Zealot Theil next to get more information about Gwyneth.
Next, you have to investigate both the Glowing Grove and Pine Crest Shrines. Take the banner pieces on each location as marked by the quest marker. Once you got the two pieces, you have to head to the Waketak Station. This is an unmarked location SW of Pine Crest Shrine so head there and enter the cabin with the lights. Pick up and play Gwyneth’s Journal holotape from the floor near the crates then loot whatever components you can find in the cabin. There’s also a radium rifle located near the journal.
Next, head to the Ruined Church, a bit to the southeast of the campground. You’ll find Gwyneth there. You can confront or kill her. You can also convince her later on to return to The Nucleus or convince her to leave the island. Once done, report back to Richter to complete the quest. You’ll also receive Atom’s Judgment.