Two things first. What rail website are you looking at for the quote of 185Euro? Second, how hold is your child? Trenitalia shows children fares from ages 4-12 but does not state anywhere how much the fare is for children under 4. I haven't included child prices in my quotes below.
Next, I'm looking at the Trenitalia schedule for 7/26 and I see a fare of 146.40Euro for two on the fastest and most expensive Eurostar Alto Velocito train. The journey takes just under 7.0 hours with no train changes. For the Italian Eurostar, the cost for two is 135Euro. The journey time is about the same but there is a train change in Rome.
If you can learn to look closely at the train schedules, which is easy on www.trentialia.com, you will see about 3 train runs a day that are in the Intercity (IC) train category. This is a lower and slower train category. These runs take 8.5hrs for the journey because they stop at more places. The trains aren't as nice as the Eurostars but the cost for two is 110Euro.
CLICK HERE to see what I see.