Italy train rail kids discount

Trenitalia has lots of discounts for families, including "Famiglia" and "Bimbi Gratis". Info is at:
https://www.trenitalia.com/en/offers.html
When you search a route at Trenitalia, put in the number of adults and children and it will automatically show you the lowest price type of ticket to purchase at that time.

Remember that Naples to Sorrento is on a private railway (Circumvesuviana) that is not part of any rail pass and will have its own child ticket prices.

The First way to save money is comparing the prices of the 2 competing railway companies: trenitalia.com/en.html and italotreno.it/en.

Italotreno runs only high speed trains between Venice and Salerno, stopping at Bologna, Florence, Naples and Rome along the way. Italotreno's discount codes are a real bargain, just subscribe their newsletter.

Second: be aware that a child can travel with any type of discounted ticket, you can always choose the cheapest option. For example, If 4 SuperEconomy tickets are cheaper than the Bimbi Gratis offer on that day, you are free to buy 4 SuperEconomy tickets.

Finally, since you are travelling up and down the boot: learn the correct spelling of the places you are visiting, find them on a map and check the prices of open jaw air tickets. I'd fly into Venice, out of Rome and I'd forget Sorrento (that, as a side note, is served by trains not covered by any pass).

Note that Cinque Terre is the name of an area made of five (Cinque in Italian) villages. You'll have to pick a village where to stay and put that village's name on trenitalia.com

Thanks. That is helpful information. I did try and price the differences and it seems like a rail pass is cheaper with kids, but I was reluctant because so many people say they aren’t worth it. And because we are going to places like Sorrento where the rail pass won’t be of use.

If you are right you'd be the first who saved money with those passes. No local has ever thought of buying one, but... better for you!
Did you add the cost of seat reservations you'll have to buy at the counter before boarding any high speed/long distance train? It's 10 € per person per leg on all Freccia-something trains. 3 € to reserve a seat on Intecity trains

To add to what Dario said, your regional trains and Fr trains are not included on the days you take day trips. They're only unlimited on days of travel.

Don't make the mistake of using one of your pass days for travel on a regional train.