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Sorrento to Naples Hydrofoil - May

I will be in Naples May 5-May 9th (approximately). We are thinking of taking an early hydrofoil from Naples to Capri, then Capri to Sorrento to tour the Amalfi for the afternoon. One, don't know how feasible that is time-wise. Two, and more importantly, is there a Hydrofoil from Sorrento to Naples?
Three, are there recommendations (and pricing) for private driver services for Naples through the Amalfi Coast for a day?