It's all a matter of taking what the adventures collectively give you and running with it.
My sandbox campaign is structured pretty similar to your excellent example. I think this is best illustrated by our last session just this Sunday:
The players were asked by an npc to investigate a local pirate captain, who had been acting 'strange' as of late. They also learned that this pirate captain had recently sank a diplomatic ship that was sent by an evil emperor. An emperor I should add, who is notorious for his cursed peace offerings.
The players located the wreck of the ship and searched it, only to find that its cargo was missing. Of course the players now suspected the suspicious captain of taking the cursed cargo (a deliberate bit of misdirection on my part).
But upon visiting a local museum (where all pirate captains displayed their glorious finds), they learned that the curator of the museum had suddenly fallen quite ill. Had the captain sold the cargo to this curator perhaps? They also learned that the captain had banned anyone from visiting the site of the shipwreck, thus further raising suspicions on the captain.
They visited the house of healing to have a word with the curator, and to undo the curse. While they were able to remove the curse, they were unable to undo its aging effect, which had reduced the curator to a dying old man. But the curator then confessed to the players that he had defied the captain's orders, and taken the cursed cargo himself, in order to become immortalized in the halls of the museum. This meant that the captain they were suspicious of, had sank the ship before knowing its cargo was cursed, and rightly so. Which painted the suspicious captain in a more positive light.
The players debated amongst each other whether the suspicious pirate captain was really a bad guy, which was exactly the sort of confusion and chaos I meant to instill in them. They also asked the curator for permission to place one of the museum's artifacts in the moonlight, believing (rightly so) that the moonlight may unveil a hidden message.
But unbeknownst to them, all of these details tie back into the main plot involving the suspicious captain. I closed the session with an intimidating confrontation between the pirate captain and one of the pc's, thus once again igniting their suspicions of him.
It's all a big manipulative game, where I try to constantly throw out red herrings, and keep them guessing. But I think the most important element in this, is that the players chase down various sides of the plot themselves. I do not tell them where to go. But I make sure to include lots of interesting things for them to chase, and I make sure there are enough hooks to tie it all back to the main plot, so that in the end it will all make sense.