Hello there BK. We had an absolutely fabulous time. We had a flat for 7 nights near Positano and stayed one night in Naples, one night in Ravello and one night in Maoiri (all in Hotels).
There were however a few buts.... first of all we were unlucky in that it was unusually hot (30C+ every day).
The plus points are that the scenery was absolutely stunning, the locals fantasically friendly and the food superb and amazingly cheap. Day trips to Pompeii and Capri were fabulous. We absolutely loved Ravello, were a bit disappointed by Positano and liked Sorrento. We also loved Naples although the local population's driving habits made Palermo seem orderly in comparison and it is without doubt, a dangerous city in terms of crime.
In general my reservations for visitors with small children relate to accessibility and convenience. The roads are very very windy so an 8km drive takes a long time and can be quite frightening, not to mention stomach churning. One thing that suprised us was that the beaches are not great and are relatively few and far between. Most are covered in black pebbles which in 30c were too hot to walk on without shoes. Parking is also a problem as it is hard to find and very very expensive. Our garage was around 300 metres from our flat which seemed pretty standard but when you are pregnant with 2 small children and it is hot, feels like a long long walk.
Ravello is one of the most beautiful places I have ever visited though and I would love to rent a house there for a week sometime.
We would have really struggled without our ATP and Pompeii was virtually impossible to get around with any buggy. So in conclusion, if you want good food, amazing sights (in both archaelogical and scenery) and don't mind a bit of hassle, I would recommend it. If however, you are looking for a beach based relaxing break with no hassle and where you basically want to stay put, then it isn't ideal.