Where do I get three sticks?

Hint 1 of 16:

Have you seen anyone using sticks in the game?

Hint 2 of 16:

There are three of them -- all identical.

Hint 3 of 16:

How about the croquet mallets in the garden?

Hint 4 of 16:

You need to find suitable replacements for each of them.

Hint 5 of 16:

That is, long objects with some kind of head.

Hint 6 of 16:

All of the replacements are animals.

Hint 7 of 16:

You can take a flamingo from the wandering shop.  That's one.

Hint 8 of 16:

And there's a hammerhead shark in a net on the docks.