Agree with above.
A.) you don't have the time to see all 3. Your time allows proper Not Excess time for the 2 you already planned.
B.) they don't mix all that well anyway, given how far apart the Amalfi Coast and CT are it is not convenient and doesn't really make sense to travel far from one seaside destination to reach another seaside destination where you will be doing more or less the same things.
Do Rome and Amalfi Coast this time and then next time pair CT with Florence, elsewhere in Tuscany and/or Venice.
For Rome and Amalfi Coast it is best to fly into Rome and out of Naples if that cannot be done just fly into and out of Rome
Since I would say you need 3-4 nights for Rome to start and 4 nights for the Amalfi Coast I am not sure why you think you have all this excess time for other towns ; if you fly out of Rome you probably need another night at the end in Rome. That looks like 10 days right there and actually quite full on each day.
I think it is a good idea to map out your days, it helps you realize how little time on the ground you actually have.
Consider it basically wipes out a full day traveling from Rome to your destination on the Amalfi Coast.
Flying out of Naples saves you a full day so compare extra cost of airline to another hotel night and extra transportation costs to get a better sense of the cost of your open jaw option.