User blog comment:Woohoot/Sunny crew/@comment-5386071-20150720031114/@comment-26082375-20150720073202

The morning of the events on Dressrosa, the newspaper announced Doflamingo's resignation from the Shichibukai. Law then called Doflamingo to set up the trade for Caesar: "8 hours from now, on the southeast beach of the uninhabited island north of Dressrosa, Green Bit! At 3 in the afternoon, we're leaving Caesar there. Pick him up whenever you like." The rest is history.

As for how much time Luffy was separated from the other Straw Hats, I forget. At least one night passed on Amazon Lily, I don't remember how much time was spent sailing to Impel Down, and then Luffy spent around 18 hours being treated for Magellan's poison before finally getting to Marineford. I would guess that's more time in-series than what has passed on Dressrosa.