weather is lovely in september and italy certainly doesn't lack beaches!
what about the italian riviera? that's on the north west coast. You can get cheap flights with ryanair to genoa or pisa and drive from there.
or you have the adriatic coast in the north east (ryanair go to pescara and ancona)
IMO driving from naples to rome and florence with a 2.5 yo and a baby might be a bit much
My mum lives there, I'll ask for her advice