What happened in Chapter 19 of The Lightning Thief?

In the Underworld the heroes learn about the fields of Ashphodel, and Elysium (the isle of the blessed). Before they can be too curious about anything, the winged sneakers that Grover has put on start acting strangely. They start flying without Grover's direction and start pulling him away from the group. They follow along attempting to hold him down long enough to pull the shoes off. It is no good. The shoes pull Grover into a cave that opens into a very wide cavern. One of the shoes comes off of Grover's feet and shoots down into the cavern while Grover holds on for dear life to the sides of the cave. Both Annabeth and Percy manage to get the other shoe off and they get to safety. Once outside of the cave Percy tells the others that the backpack that he's carrying has become very heavy. He is embarrassed to admit that, but all time for bravado has left them. Suddenly they hear a whisper coming from the cave and they realize that it's the entrance to Tartarus.

They make their way to Hade's palace, made of Obsidian stone and guarded by the skeletons of dead soldiers. When they reach Hades, Percy calls him 'Uncle' and this further angers Hades, who accuses Percy of stealing not only the bolt, but his Helm of Darkness. Percy denies it, but Hades doesn't buy it. He calls Percy a liar and says that the bolt is right there, in Percy's backpack. Percy adamantly denies this but opens up the bag to reveal....the bolt. Percy has no idea how the bolt got in there and he and the others begin to fear for their safety. Hades tells Percy he will barter the Helm of Darkness for his mother's life. He says she isn't dead, yet, but that she can be if Percy doesn't come through. He asks Percy to show him the transport pearls that Poseidon has given him. Hades tells him that he must choose whom will remain behind, but Percy makes the choice to leave his mother behind, and to return for her at another time. They break the pearls and escape to Santa Monica Beach. He knows who has set him up and they determine to find Ares as soon as possible.