Otello alla Concordia is just off the Piazza di Spagna and can handle big groups. We had a very good lunch there.
A big pizzeria in a residential neighborhood would be perfect, they’re used to big families. I don’t think there’s anything of that sort in the high-rent Piazza di Spagna area.
L’Antica Birreria Peroni is a fun place for groups and kid-friendly.