if you don't have your heart set on Sorrento, I'd reconsider. It's nice for a day but very touristy for anything longer.
Travelling independently can work out cheaper and you don't have to compromise as much on what you want yourself. However, the searches can be time-consuming.
The nearest airport for Sorrento is Naples but the flights there are less frequent and more expensive. Aer lingus is a more comfortable and relaxing airline to fly with with children but the cheapest flights to Italy are generally with Ryanair. The nearest they go to Sorrento is Rome (Ciampino) Rome, you can get a train to almost anywhere in Italy.
If you're not too fussed about Sorrento, you mght consider Bologna (Aer Lingus) or Forli (Ryanair) and getting somewhere on the Adriatic coast (e.g. Riccione or Cattolica). They're more like regular seaside holidays which might not tie in with the purist's vision of Italy but have much more to do for children. The train stations in both forli and Bologna are easily accessible from the airports.
If you want to book hotels directly, try venere.com or hotelclub.net.
Best of luck.