Is there a particular car (carriage) I should book, since the site asks? We have a 1 year old and I didn't know if Eurostar AV has a "family" car. Also, do you have assigned seats even in second class? This is the Rome to Venice route.
IF seat reservations are require, it is required for second class.
Eurostar will assign you a seat when you purchase your ticket - no matter what class of service you select. Intercity and Regionale trains do not require a seat reservation - it's open seating on those.
A few of the EA trains I have been on do have what they call a "family" section, most frequently located in the first and last coach - But these ONLY entail seating for 4 around a "fold-down" table (as opposed to a "fixed table")...not really much different than regular seating on these trains.
Children under 4 do not need a ticket but will have to ride on your lap ... unless your part of the train has "empty" seats. If you would like a designated seat for your 1 year old you'll have to buy it. Children seats (4-12) are one-half the adult fare. It's about a 4 1/2 hour ride from Rome Termini to Venice S. Lucia. Hope that helps!
Ciao,
Ron