Loving that "squirmy luggage" comment too!
Your baby will be perfectly "safe" in Italy and will be happily accepted everywhere so I don't think that's the bigger issue. As already mentioned, the larger consideration will be the logistics with a child that age and all the accoutrements they require? That can add up to a lot for two people to have to handle on and off trains and up and down stairs... There are lots of stairs in Italy, and lots of steep slopes in the Amalfi area. Some parents have done OK with a stroller (I'd take a lightweight one but with GOOD WHEELS) where others swear by back carriers: easier for stairs but an 18 month-old is pretty heavy. Some do both but there again, lots of stuff to manage. A car seat adds to the mix.
But all that aside, have you already done a reasonable amount of travel with your tot outside of just driving from one place to another? I'm thinking of things like being confined in a plane for long hours, going to sleep easily in the same room with you, and general adjustment to new places?
You know your baby best so really, it comes down to how well you think she will manage and how well YOU can manage all her stuff AND your stuff. I do think that the less moving around you can do, the better, and I'll go along with 1-nighters not being worth the hassle of picking up and moving.
It goes without saying that your schedule is going to revolve around hers, to some extent. That day you intend to spend doing wineries on an organized tour could be the day she decides when enough is enough - earlier rather than later - so I would keep your days as flexible as possible
Maratea: much too far from the Amalfi area and a long way back to Rome. I'd scratch that one, personally, or settle in for a good long stay.