Hi Sarah. I agree with staying in one place in Tuscany & then visiting Florence, Siena & Lucca as daytrips instead of moving around so much. Siena would be in between Lucca & Florence but keep in mind that Lucca is a good 2-hr drive from Siena so you'll spend 4+ hrs driving to/from Lucca plus time to find parking, etc.
I would recommend taking the train from Rome to Orvieto on day 3 or 4, sightseeing in Orvieto all day (it's a cute town) & then renting your car there to drive to Tuscany. We did this and we stayed near Siena in an agriturismo. From Siena, you can easily do Florence as a daytrip & then maybe a few of the closer hill towns instead of Lucca (maybe Montepulciano, Pienza, Volterra, etc.) If you stay somewhere near Siena then you can return your car in Siena & then take the train to your next destination. You don't want to rent or return your car in larger cities like Rome or Florence...it's a nightmare.
I don't think one day is enough time in the Cinque Terre. I just returned from there & I took the advice on many on this forum & spent 2.5 days there. I could have easily spent another night & full day there. One day isn't enough to do it justice. So, I would cut out the Cinque Terre & maybe travel straight to Venice after Tuscany.
I agree with the previous poster that if it's your first time in Rome, 2 full days isn't enough. I would cut out the Cinque Terre & add that time to Rome.