Venice to Sorrento (Stopping in Napes/Pompeii)

Becky, the problem with your question is the quality of visit you want to make in Naples and Pompeii. Neither of them are quick stops if you want to do them any justice. There's no way I'd try to do all of it in one day from Venice as you are at least 5 hours + by fast trains (there is no better, faster way than these trains) JUST to Naples.

What is it you want to see/do in Naples?

I agree with Kathy. The fastest way from Venice to Sorrento is by train, and requires a change of trains in Naples. You did not specify what you wanted to see in Naples, but I will agree with Kathy you don't have time for much on top of your travel that day. It's only about an hour from Sorrento by train, and the fare is inexpensive. But doing Pompeii + let's say the Archeological museum in Naples would be a full day all by itself. I'd recommend this as a day trip from Sorrento.

Hire a private jet or buy a water taxi express to the Venice airport and take a public airline Easy Jet
https://goo.gl/flights/wDJy6
fly to Naples in an hour.

Rent or hire a private car to drive you from the airport to Naples and the on to Pompeii before you go to Sorrento
It is simple.

Backing up a little, it is entirely possible that you could shave some time off the Venice>Naples piece by flying but by the time you mess around with airport processes, I don't know just how much that would be. It's possible, though, and it may even be cheaper if flying a budget airline. You'd have to check frequency of flights and fine print on extra fees, although you did say money wasn't a consideration.

water taxi to Marco Polo, then taxi or private driver for the day from Naples airport. What do you want to see/do in Naples? That could slow you down significantly because of really bad traffic in the city. It might be better to go straight to Sorrento and stop in Naples on your way to your next destination.

If you have an unlimited travel budget, then you really don't need to travel in such a rushed way. Spend the budget on more days on the ground so you can do these places justice without the need for speedy transport. Quality and slower pace over quantity.

Fly. It's like $50 to fly to Naples Airport. (On easyJet)

From airport hire a private driver to take you.

If you have unlimited travel budget

Given this premise, private helicopter