Travel from Florence to Positano

Jill, I'm unsure what sort of alignment issues you're having? You can take a ferry from Salerno to Positano. Current schedule is here:

http://www.positano.com/en/ferry-schedule

You shouldn't have an issue being able to get to Salerno by train in time to catch any of the last three runs? I'm seeing direct trains from Firenze SM Novella to Salerno in as little as 3 hours/16 minutes and others for at or under 4 hours. I would do this route versus try to take boats from Naples as there are no direct ferries from Positano from there.

Don't rent a car: absolutely no need to do that.

Editing to add: the one caution would be if your travel day ends up to be stormy or very windy. The ferries cannot dock in Positano if the seas are too rough. Your alternative by public transport from Salerno would be SITA bus, and it would take some time.

You also have the second option of high-speed train to Naples, local Circumversuviana commuter train to Sorrento and ferry, SITA bus or private transfer from there: more messing around but would offer alternative options of getting to Positano (bus or private transfer) if the sea doesn't cooperate. Current ferry schedules from Sorrento:

http://www.positano.com/en/ferry-schedule?from=sorrento&to=positano

I think your best choice is taking the Freccia train Florence SMN to Naples Centrale (just under 3 hours), then hiring a driver to take you to Positano (1 hour but maybe a little expensive). Otherwise (as Kathy said, just saw that!) it's the Circumvesuviana train Naples to Sorrento (1 hour), then transfer right there to the bus that will take you Sorrento to Positano (1 hour). With bags that might be a P.I.T.A., but is doable.

Ferries are weather-sensitive and I wouldn't depend on them as my Plan A.

My .02. Enjoy your planning!

Driving all the way from Florence may make sense if you have multiple passengers with luggage and also intend to keep the car in Positano.

But if you plan to catch a boat from Salerno or private driver from Naples or use public transportation all the way to Positano, a train will get you there faster than a car. A train can get you to Naples in less than 3 hours (or slightly longer to Salerno). A car will need 5 to 6 hours once you account for pit stops.
Train to Naples or Salerno:
www.trenitalia.com
Train Naples to Sorrento:
www.eavsrl.it
Bus Sorrento to Positano:
http://www.positano.com/en/bus-schedule

See above post by Kathy for boat schedule from Salerno. Be aware of the possibility of no boats not operating off season or with rough seas.

I'd take either a trenitalia.com or an italotreno.it direct high speed train to Salerno, followed by a ferry.
Ferries are weather sensitive, but it rarely happens in summer. If it actually happens, there are buses and cabs to reach Positano.

Compared to a bullet train, a car from Florence would be excruciatingly slow and boring untill you reach Naples, than a traffic nightmare from the moment you exit the A1 motorway.