If you weren’t needing to take a train back to Florence that evening, I’d have several other restaurant recommendations, especially a bit south of Termini station in the Testaccio neighborhood. But you ask about a “better dinner experience.” How much better will things for your toddler, and will that influence how good an experience it’ll be for the rest of the family? Earlier will make everybody happier in the end, I suspect.
Italy’s not Spain. And dinner at 5:00 vs. 6:30 doesn’t quite mean you’re having dinner while everyone else is just finishing lunch. But if you want an actual Italian place, and aren’t counting on a 3-hour meal lasting well past dark, you still have options close to Termini. Last fall, I stayed at the Deco Roma UNO hotel, 2 short blocks southwest of Termini. There was a decent restaurant just across the street, at Via Giovanni Amendola 26. They had tables on the sidewalk, but it was less hectic inside. Their gelato was fantastic, by the way. I couldn’t have told you the name, and there’s no big name signage out front, other than simply “Pizzeria, Bar-Gelato, and “Ristorante” and looking it up just now, I’m surprised that Google Maps says it’s “King Food Termini.” Not a stellar name, but the food’s good, it’s super convenient, and they’re open 24 hours, as could be expected from a place a 3 minute walk from a European capital train station. If you’re looking for an intimate Roman dining experience, there are other places on the street, but consider dining here.