Italy for Daughters graduation add Switzerland or Greece?

Save Greece for another time since it is little further away from Italy; and you are planning to spend 3 days in Switzerland so that is not too bad on the budget.
Forget staying in Interlaken the scenery i.e. mountains, waterfalls, little villages are easier to access staying in around Lauterbrunnen.
And Monterosso in Cinque Terre is where the largest beach can be found among the areas in your itinerary.

You probably will get advice to cut something of the areas you have here; and I agree.

That is a very fast paced trip. Assuming you have 14 nights sleeping in Europe, you have 13 days to enjoy your travels. So "Interlaken 1 day" is really 2 nights/1 full day. You have outlined 7 places for 2 weeks. That is an average of 2 nights in each place, so one full day. When you change locations (i.e., Florence to Rome) although the train trip is only 90 minutes it will take you half a day to pack, check-out, get to the station, take the train trip, find your new hotel. By then it is time for a late lunch and you have perhaps 3 hours of good sightseeing time left in the day. And with frequent changes comes expense for transportation between places.

Thinking about how many nights you are going to sleep somewhere helps frame the time you have. In other words, something has to go.

If you want to do Switzerland and Italy, I suggest two stops in each country. Luzern and Lauterbrunnen (a bit beyond Interlaken but a far superior place to stay as Interlaken is rather dull) and pick two of the Italian locations. Also, Geneva is nothing compared to the Lauterbrunnen area.

Perhaps something like this:

Fly to Zurich and immediately take the train to Luzern. Stay 3 nights. Gives you two FULL days.

Train to Lauterbrunnen, stay 4 nights/3 full days

Train to Venice, stay 3 nights/2 full days

Train to Rome, stay 4 nights/3 full days

Fly home from Rome. (Or go to the Cinque Terre and Venice, Venice and Rome, Cinque Terre and Rome, Florence and Rome -- just pick two and fly home from the last city.)

I know nothing of Greece, but flying between Rome and Athens, for example, will probably take you about 8 hours door-to-door by the time you have airport transfer and waiting time.

Jazz and Laurel are right: Just too many places with no time to breathe. I like Laurel's real-world suggestion, which will allow time to appreciate the cities and towns on your itinerary rather than just train stations.

If you can't bear to cut any of your Italian destinations, that's OK, but Switzerland will need to go. And if you can scrounge an extra day or two, that will help. The first day in Europe is of marginal value because of sleep-deprivation and jetlag, and the last day is totally worthless since you'll spend it flying back home.

2 weeks is not enough for all of that. Greece would be worse because you waste a lot of time to fly there. Plan nights, not days, try to stay at least two nights at each location (3 nights in Rome at the very least).it will be very rushed but at least you have time to unpack your suitcases.

Take time to enJOY and experience. I'd cut it to ONE country. We spent 3 weeks in Italy - Venice, Florence, Rome, Sorrento and barely scratched the surface. 1-2 days in Venice is not enough, we spent 5 and can't wait to return. Neither is 3 days in Rome- you want to do the Vatican, Colosseum, Forum, Pantheon, Trevi Fountain - and we did 2 walking food tours with EATING ITALY that were fantastic. You need more time in Florence. Take 3-4 days to see Florence and then take some day trips into Tuscany - we used 'Walkabout Florence' - we did their BEST OF TUSCANY and CHIANTI WINE & FOOD SAFARI - amazing - see reviews on TripAdvisor and then check out their webpage - we loved the way they did Tuscany!!! We chose Herculaneum over Pompeii after reading tons of reviews . . . followed RS book and LOVED it. Took the train from Sorrento. I say fly into Venice, train to Florence w/day trips to Tuscany, train to Rome, Train to Sorrento w/day trip to Amalfi Coast - (Cinque Terre in ONE day is NOT enough) and a day trip to Herculaneum or Pompeii - then fly home from Naples. It is your vacation, but you will not get a great experience at that pace. Europe is to be savored. Don't forget, traveling from city to city and checking into hotels before you can even begin exploring takes LOTS of time.

chinalake67 and all, thanks so much for great feedback- ok total change, flying into venice(only place I have been to prior stayed way to short of a time and cried when had to leave) and flying back from rome.
Itinerary:
, venice 3 nights, cinque terre 1 or 2 nights; florence 3 nights and rome 4 nights.

Antyhing to change on intinerary?
just booked venice at hotel galleria, only will book hotels i can cancel since not leaving till 5/21 and something could come up. Love that chinalake67 said tuscany tours and eatitaly- any other must do unique for mother daughter or my 21 year old who won't be much into museums- but we will do a few.
Comments
Venice; Row Venice? Best eating/walking tour in Venice focusing on drinking wine more than eating? suggest visit to Burano? Is it worth taking boat/water taxi from airport if my hotel is close to drop off? kind of $$ but maybe worth it?
Florence: have some recommendations from chinalake67 on tour- eating and walking- what about Vespa rental?
Cinque Terre- 1 nights not enough, 2 nights too much? see rick steeves suggests going from venice to CT then to Florence but some suggest venice to florence to CT then to rome- suggestions?
Rome: any great day tours , coworker suggested golf cart tour, kind of pricey.
Any other wonderful unique ideas ?

If you want to get to Monterosso (randomly selected Cinque Terre town) from Venice before 2:38 PM, you'll have to take the 7:25 AM departure. I wouldn't be up for that, but perhaps you are. That early train gets you to Monterosso at 12:53 PM after a couple of transfers. The 8:47 AM departure arrives at 2:38 PM after three transfers.

As you can see, one night gets you pretty much nothing in the Cinque Terre when traveling from so far away unless you plan to depart quite late the next day for Florence. There are roughly hourly afternoon departures from Monterosso until 5:20, then the next train is at 7:05. Most of the trains take about 3 hours; the 7:05 is a bit faster. You'll always have at least one transfer.

Those times are for weekdays this month; there may be some variation in May, and certainly weekends (especially Sundays) can be different.