First two weeks of Sept in Italy: Sardinia or Sicily, plus Naples + Almafi coast?

Sardinia and Sicily are both quite large, so to include them in a two week itinerary with something else will require some careful selection--either could be your two week trip. I would hesitate to pair them with the mainland.
You seem to want a slower paced trip, so I would suggest you consider how leisurely a two week trip to Naples, the Amalfi Coast, and the islands just offshore could be.

I see. In that case, we need to decide between an island only or only Naples + Almafi coast...

Well not necessarily, some might still want to include both. I am just alerting you that a lot of decisions have to be made for what to include or eliminate and how much travel to include.
Make your list of preferred destinations among all three areas and see what rises to the top. You could also add the Cilento coast south of Salerno, where there are some very fine beaches (better than what you will encounter on the Amalfi Coast). It makes a nice pairing with the Amalfi area which is so crowded.

Go to Sardinia if you are looking for some beach time.

We were there the last week in August, and we had a fantastic time. Weather wise it was not too hot. We had just beach days, and other days we would visit a somewhere in the morning, then hit the local beach in the afternoon. For example we visited Oristano, then went out to San Giovanni di Sinis for a lunch on the beach. Them some of us went to the beach and other visited the archeological ruins.

It seems to me that if you were to go to Sardinia for a few days, you could probably skip the Almafi coast, and dedicate more time to Naples.