Just my .02 (I’ve lived in Italy) but you and your kids deserve to see more than the inside of a train station or a train…
You could spend 10 days and just scratch the surface in and around Rome. Why not get an apartment in Rome for 5 days and Florence for four days and (if you feel the urge)make day trips to places like Tivoli, Pisa, Assisi, Arezzo, Lucca, Fiesole,or Siena etc etc etc etc?