You don't need the Yellow Trinity to beat Neverland.
The Yellow Trinity in the cargo hold just leads to a room with a few treasure chest.
You need to win the Hercules Cup to get the Yellow Trinity, but in order to unlock the Hercules Cup you need to seal the keyhole in Neverland, it becomes available after that.
The events in Neverland break down pretty much like this:
-Reach the pirate ship, an event with Riku occurs, and you get captured.
-You meet Peter Pan and he joins as you all search for Kairi
and Wendy.
-When you make your way through the iced cargo hold and head up the latter at the other end there a scene with Kairi.
- After that looking at the ceiling above, a big hole
on the edge of net allows you a way to get up to the next floor where you can get to the Captain's room.
-Activate the green trinity in the captain's room. There's a cut scene and you fight with the dark Sora.
-After the battle, examine the hole near the captain's bed.
-Separate with Peter Pan (i.e. remove him from the party) and meet with Wendy in a room. After that return to the Captain's room and exit through the main door to the outer decks.
-Battle with Heartless and with the Captain Hook. You'll gain Cura magic and Ansem Report #8 .
-Now you can reach the Clock Tower. Set the clock to 12 and lock the keyhole. You'll gain Navi gumi.
-Talk to Peter and Wendy, after that you gain Tinker Bell summon and Fairie Harp Keyblade.
So basically once you seal the Neverland keyhole in the Clock Tower you can move the story along, get access to the Hercules Cup and the Yellow Trinity once you beat it.