Our itinerary is pretty full but we want to do more in less time.
In order to "do more in less time" and maximize your touring time, I'd suggest scratching the idea of using a rental car and stick with trains (high speed trains whenever possible), especially with such a VERY short time frame. Note that each driver would require the compulsory I.D.P. and you would have to be VERY careful to avoid the dreaded Z.T.L. areas (hefty fines for each pass through one of those). Does the 12 days include your two travel days?
Regarding your last Itinerary....
- Rome 3 nights - sounds good.
- Florence 3 nights - I'd suggest adding one of the Milan days here. Florence is in Tuscany and it makes a great home base for touring the area. One popular trip is to travel by Bus to Siena as it's only about an hour each way.
- Cinque Terre 2 nights - as you're travelling in early July, I would HIGHLY recommend getting some accommodations booked SOON in the C.T. (especially with two couples). It may already be too late but I'd suggest starting in Monterosso as it's the largest of the five towns and therefore has the greatest number of hotels. If you can't find anything in the five towns, you could try Levanto. The Guidebook has good listings in all of the towns.
- Lake Como 2 nights - the usual favourite with many here is the small town of Varenna, which is only about an hour from Milan by train. Again, the Guidebook has lodging suggestions, but you could start with Royal Hotel Victoria, Albergo Milano, Villa Cipressi or Eremo Gaudio. If you'd prefer to stay in Bellagio and have a "generous" budget, you could have a look at the Grand Hotel Villa Serbelloni. Bellagio is an easy 20-minute Ferry trip from Varenna.
- Milan 2 nights - unless you have something specific to see in Milan (ie: Last Supper), I'd suggest using one of these days elsewhere. I'm assuming you'll be departing from MXP for the flight home?
There are also some potentially expensive "caveats" to be aware of when using trains and other public transit in Italy, so it would be a really good idea to do some "homework" on that point.
July is PEAK travel season so you may have to adjust your budget "upwards" for short notice hotel bookings in all the places you'll be visiting.