I dont know if you have stumbled across
http://www.trenitalia.com/en/index.html yet, but it is the website for the Italian passenger railroad, TrenItalia. A quick glance of the schedules dont look like they may be best for you, but I would suggest looking and playing around with timetables and see if there is something that might work.
I've never driven in Italy, nor have I traveled direct from Milan to Rome on the highway. Maybe some others can take the topic of renting a car?