14 nights southern Italy including Rome,Naples,Sorrento, Almafi, Bari, Silcily

How many days in Rome? Write out the rest day by day, and I think you'll find that something has to go.
If you have not booked the Amalfi coast for this April, it could be difficult to get accommodations already, so that would be an easy one to cut, giving you a more realistic amount of time for Rome-Bari-Sicily (which will still be tight, but if you are very selective with Sicily, at least doable).

This is somewhat what we are thinking.
Day 1 Rome
Day 2,3,4 Sorrento area with tours to Pompeii,Naples,Sorrento
Day 5,6,7 Drive to Bari and see parts of Puglia Area
Day 8 Drive to Reggio Calabrian to get ferry with car to Sicily
Day 10,11,12 Sicily
Day 13 Fly to Rome
Day 14 Rome
Day 15 We fly home out of Rome

That is doable--you had Amalfi and Capri on your initial list, hence my skepticism. Would I do all this? No, but it does work for someone who likes a fast pace. One thing to sort out quick will be whether you can drop the car in Sicily. Where in Sicily are you headed? If it is on the east coast, that will work better.
Near Bari, I would see Matera and the Itria Valley.

Most would say that 14 nights is barely enough for Sicily.

Have you considered doing this in reverse?
Fly right to Sicily on arrival to Rome (rather than a Rome 1 nighter)
3-4 nights in Sicily- where exactly did you plan to go?
Check to see if you CAN take a rental car on ferry- not sure you can.
Then to Bari 3-4 nights
Then to Salerno or Naples and drop the car. You won't be using it or need or want it while in Sorrento.
Sorrento- 3 nights (or just stay in Salerno or Naples- wherever you dropped car- since you want to visit Naples I'd stay IN Naples.
Back to Rome- you did say you are not interested so much in Rome this trip so give Rome 2 nights at end- give the extra days to Sicily.

I'd Drop the car in Bari and fly to Sicily. Or viceversa if you are going to follow the good advice above

The southern road along the foot arch is really awful and it will make you waste lots of time. It would also put any relationship at risk.

More, around Easter, the lines of cars at the docks to/from Sicily are horrendous.

Most car rentals prohibit ferries. You don't want to drive inside Naples.

Parking in Sorrento is tedious and expensive. Cars are useless on Capri.

Day 8, driving from Bari to the Sicily ferry in Messina, takes 5 1/2 hours before you even get on the ferry. We drove from the southern tip of the heel to Sicily, but chose to overnight along the way. It was still many hours in the car. Yes you can take your rental car on the ferry. We had Avis and made sure before we left. Also, buy your ferry tickets online before arrival at the ferry. We didn't and missed the first ferry because the signs were so confusing (a marital test for sure!) and absolutely every other car had mobile tix.

Yes to Matera!!!

Also, google had us drive the northern coast, along the foot top, and it was truly spectacular.

I agree with changing the order.

Power through and fly to to Sicily after landing in Rome. Rent a car the next day. Enjoy Sicily.

Return the car and fly to Naples. You do not need or want a car in this area. After your AC visit,
rent a car to get to Bari, keep it through the remainder of the trip, turn it in outside of Rome, Tiburtina Station(?)
Train into Rome.

The main concern at this late date is accommodation availability and the ability to get some of these flights. And where are you going to be on Easter? You might have to work backwards and see what you can get, first, and then map it out. Sadly, you might have to eliminate some locations.

Thank for all the input so far!
We are thinking seriously about changing the order and possibly adding flights once landing in Rome. Not sure of the order yet. It will depend on availability for flights and rentals.

Sunny22-If we went with renting a car in Rome and driving to Bari and back to Rome, would you take the same route each way?

I am not familiar with the Bari area or the drive there. I usually would recommend a different route each way for interest, but those with experience would be a better resource. But we do love having a car, to be on our own schedule and find special locations off the beaten path.

We were in Venice one year a few days before Easter, and it was extra crowded , beginning on Good Friday thru Easter Monday. The vaporettos were jammed , even at night. Note that many businesses are closed Easter Sunday and Monday, that the small towns are very quiet, and wineries are closed.
Again, I'll repeat what others have said-
Check for accommodation availability- many here are reporting high prices and low availability for lodging. There's significant pent- up demand. If you can't find a place to sleep in a area , you'll need to modify your itinerary. You really don't have much time before your trip to make reservations.
Safe travels!