ABSOLUTELY do NOT waste time on such a short trip just to return to your point of entry to fly home! You should be able to open jaw this trip, with little or no extra expense. Even if it costs a little more this way, consider the savings on not taking that train trip back (not to mention your valuable time). Fly into Rome and depart from Venice, or vice-versa.

DEFINITELY skip Pisa. It's just not worth it on such a short trip! If you MUST add another city, it should be Siena (easy half-day trip from Florence). Although the country is compact, you are moving around far too much with your planned itineraries...

My advice, if you only have a week:

July 2: Land in Rome (adjust -- you won't be able to see much)
July 3: Rome
July 4: Rome
July 5: early morning train to Florence
July 6: Florence
July 7: early morning train to Venice
July 8: Venice
July 9: depart for U.S.