we just did a 12 days roundtrip on Sicily this March with our 4 months old daughter.
We originally planned to stay in max 3 different places, but ended up changing accomadation daily. This way, driving distances are shorter, because you only have to go in one direction and not back.
We started in Catania (2 nights), made a nice trainride around the Aetna, went then to Milazzo (2 night) with a dayrip to Vulcano, Lipari would be also suitable, then its just a short motorway drive to Cefalu and Palermo, from there we hid south to Agrigento, back into the mountains to Piazza Armerina, and spent then a few days in the Val di Noto. We chose Ragusa and lemonfarms near Noto to sleep.
Before we ended the tour we still visited Syracus. So in total, we visited 7 WHS sites in 12 days, The car rides comparably short and whileour baby was sleeping, we booked the nights spontaneously (hotels, Agriturismo, and AIrbnb), accomodation was cheap, rented car even cheaper, and in Sicilly the people love small Bambini, so you are welcome everywhere.
Our tip for traveling WHS with a little baby!!