Rome 3 nights, cortona area exploring Tuscany 5 nights, Florence 2 nights, CT 3 nights, Parma visiting family 2 nights, Venice 2 nights.....
It's reasonable, but if you're on such a short trip, I'd subtract one night from the CT and add it to Venice.
I'd suggest cutting back a night in Tuscany and adding a night in Venice; and just a suggestion- in Venice, get your room somewhere other than the track between san marco and the rialto- if you don't, you'll be constantly in a crowd; a few blocks away, and venice gets quieter and better.
In your prior posting, you mentioned several Tuscan towns you wanted to visit. Cortona is on the extreme eastern edge of Tuscany. A more central Tuscan town, like Montepulciano or Siena, might be a better base. If renting a car for Tuscany, take the 1 hour train ride to Orvieto and pick it up there - easier and less expensive than renting in Rome. You can then drive to Civita before going on to your Tuscan base. If train connections between CT and Parma are awkward, consider driving to Parma right after Tuscany and then driving to CT. You could return the car in La Spezia, then take trains to CT town, Florence and finally Venice. Pisa and Lucca are also easy stops on the way from CT to Florence. If you decide to stay in Montepulciano, consider Mueble il Riccio. Terrific small hotel!
Great suggestions!!!! Thank you so much!!!!