Do i buy my kids as adults train tickets?

It depends on the type of train. Under 4 are always free.
Freccia and IC trains, 4 to 14 pay 50% of adult fare. 15 and up pay adult fare.
Regionali, 4 to 12 pay 50% of adult fare, 13 and up pay adult fare. But it can vary depending on the province.

ItaliaRail is NOT the same as trenitalia. ItaliaRail is a travel agency - resell of train tickets. Trenitalia is the national rail site.

Hello,
A great site to use is:
https://loco2.com/en?gclid=EAIaIQobChMI68W8x-qW3AIVULbACh2hVwdcEAAYASAAEgIeSvD_BwE&utm_content=Brand+Pure+-+Exact&utm_keyword=loco2+com
I used it to book train travel all over Italy from Milan to Stresa to Rome, Verona, and Venice- you can create an account as well- user friendly with great prices especially when booking in advance. The earlier you book the cheaper the ticket. There are fast trains and regional trains- first and second class (second is just as nice) and they will show you all companies ( Italo, Trenitalia) ect. Put in ages of children to see pricing.

Happy Travels✨💫

You might want to check out the easy to use Trenitalia app. I find it easier to use than the website. If you’re taking a smart phone, you don’t need to print out your tickets. Just show the conductor the codes on the phone.

Entering ages for the kids is not in the initial steps of a ticket search with Trenitalia.com. Read the details on the pop-up links to be fairly sure that your kids will meet the rules (that Sam also summarized). Then you choose a fare and read the details along side it, like Bimbi Gratis, etc, and then later you add the actual traveler birthdates. Hopefully that last step will catch or adjust any mistakes if your kid is too old.

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https://community.ricksteves.com/travel-forum/italy/train-question-italy-and-switzerland