Marie,
I've been to both and agree with many of the points already mentioned. The Cinque Terre would be a better choice in this case, especially as you're trying to reduce the number of days in your trip and it fits well for transportation to the other locations you're visiting. I wouldn't suggest doing that as a day trip as that won't provide much time to enjoy or explore the area. While Sorrento and Capri are also beautiful (in a somewhat "different way" than the C.T.), it would be better to visit that area with more time. I'm also an avid photographer, and there are lots of good photo op's in the C.T.
By dropping the Sorrento/Amalfi portion, you can add a day or two in the other locations. I'd suggest adding at least one day to Rome and perhaps one day to the C.T. With an extra day in Rome, you might consider a day trip to Orvieto, which is a beautiful and historic Umbrian hill town. With an extra day in the C.T., you could take a day trip by boat to Porto Venere, by train and boat to the glitzy resort of Portofino or even Levanto, which also has beautiful beaches. Levanto is only about four minutes by train from Monterosso, so not difficult to get to at all. There's also a trail between the two towns if you're energetic (Laurel can fill in the details on that, as I haven't hiked that one yet).
If at all possible, I'd suggest making your trip at least 14 days. The first and last day will be flight days and you'll be jet lagged for a day or two after arrival, so won't be up to full "touring speed". As this might be one of the last trips you take together with your daughters, that's something to consider. I never had an opportunity to take a trip like that with my Sons before they left home, which I regret. When is this trip taking place?
As you haven't been to Italy for 30 years, it would be a good idea to do some research on using public transit there, as there are some potentially expensive "caveats" to be aware of. The same is true with rental cars. Are you planning to travel by train most of the time?
Once you've nailed down a more-or-less definite Itinerary, I'd suggest getting some hotels booked (especially in the Cinque Terre). Which of the five towns are you planning to stay in? Would you prefer a more conventional hotel that provides breakfast, or just a room with no breakfast provided? Everyone here has their own favourites with the towns, and my favourite is Monterosso.
You might find it helpful to pack along a copy of the Italy guidebook (2015 version will likely be out in Sept. or Oct.), as there's an enormous amount of information there that will help to plan your sightseeing most efficiently. You should be able to find a copy at your local Library to help with your planning.