Trip to Berner Oberland then on to Italy

I would say a week is not enough time to see Florence, CT and Rome. You really want at least two full days (3 nights) in Florence and at least 4 full days in Rome (5 nights). Getting to CT is going to take a while, so you would want at least 2 nights there to give you a full day to explore. That’s 10 nights just for Italy.

That gives you 3 nights in Murren. I would drop CT and add those nights to Murren.

You will likely get lots of different opinions on this. Here is mine.

You have a good start with 4 nights in Mürren—-lots of good hiking opportunities there, some right from your door. The North Face trail, with its signed viewpoints of the peaks across the valley, explaining the history of alpinism (first ascents, etc.) in the area, is one of our favorites. The trail goes from the top of the Allmendhubel funicular back down to Mürren, in a broad sweep out to the southwest (I think that is the direction) and then back. Allow half a day. Lots more hike recommendations available from me and from others is you need them

For the transit to Italy, note that the two main (fast) routes go under the Alps in deep tunnels: via Spiez and the Lôtschberg Basistunnel plus the Simplon tunnel, or via Luzern and the deep Gotthard Basistunnel. For a more scenic and enjoyable trip, I suggest taking the Treno Gottardo, which goes over the Alps from Luzern to Locarno via the Gotthard Pass route, with a spiral tunnel and some switchbacks along the way.

https://www.myswitzerland.com/en-us/experiences/treno-gottardo/

You could make the trip from Mürren to Luzern (also a scenic trip) to Locarno in one day, and overnighting in this nice lakeside town before continuing on to Milan and then Florence the next day.

However you choose to travel to your Italy destinations, you will head first to Milan and change trains there for Florence.

For your Italy portion, I suggest you think about and list your goals so people can help you apportion your time wisely. I agree with travel4fun that visiting Florence, Rome, and Cinque Terre all in a week gives you too little time to do justice to all three. How important is each of these to you, and for what reason?

I personally am happy with just 2 nights in Florence, as we are more interested in archeology and historical sites than art museums. And while we enjoyed our 3 nights in Manarola in Cinque Terre, we would have been just as happy with 2, with time to hike over to Vernazza ( which was so crowded we couldn’t depart fast enough) followed by a swim from the rocks by Manarola and a walk through the vineyards there. It was too hot to do any hiking at all on the higher trails.

But if you gave each of those 2 nights each, that would leave only 3 or 4 for Rome (depending on your Switzerland time), and that is definitely not enough for Rome (we spent a full week there and never ran out of things to see and do).

Very early September is a good time to see Switzerland, after that expect bad weather. Look at lift/train passes I think 5 days rather than 4 would workout better. I would not do Rome and Florence on the same trip, pick one, too many big cities for one trip. J

Agree with Lola on Florence. It is quite lovely. We just left last week, and although we did 4 nights, 2 would have worked out fine. As for Rome, here is where we may disagree with others. It's packed. Way overcrowded which took a lot from our experience. Although having been to Rome several times, and always saying been there and done that, we went because a friend of ours traveling with us had never been to Italy and we felt obligated to go again. He hated it. Not Rome itself, just the crowds. Rome has so much to offer if you can hit it at just the right time. Every sidewalk, cafe, and tourist spot was elbow to elbow our entire time. An airline strike forced us to leave a day early, and we were all so glad to do so. This is not everyone's experience. There is a lot to see and do, but we managed to show him everything, including the Vatican in two days. He watched a YouTube video from the Roman Guy tour guide that said how to do Rome in a day, and boy he did it. Florence was not overly crowded and very enjoyable. Enjoy your time in Switzerland. It's beautiful and peaceful, and you will find lots to do. If you have never been to Switzerland, consider a night in Lucerne. There is a lot to do there as well. If you want to consider Cinque Terre, you might do Switzerland and northern Italy, and save Rome and the south for another trip. Where will you fly out of?

I will add this: To go from Lauterbrunnen to Florence will take a minimum of 8 hours of travel via train. You will need a minimum of 5 hours if you train to Zurich and fly to Florence. Either way you have nearly the entire day of travel.

Another option would be to make it a day's adventure by taking Bernina Express and then from Tirano, train to Florence. This will take the entire day but at least you will have an interesting train journey.

Lauterbrunnen to Firenze (Florence) takes 6 hours by train (well, 6h and 2 min for the fastest connection to be exact). Not "at least 8 hours" as mentioned above.
Use www.sbb.ch for planning. One advantage: You can do the whole on one booking.
If you decide to ly then it is 2h42 min. to the airport, then of course you need account for all the friction that air travel involves nowadays, so you will not really get there faster. I would take the train.

I'd strongly consider the travel time that will be lost. I know there is an argument for packing it in while you are overseas, but two week would be perfect for Rome-CT-Florence. Switzerland plus Rome or Florence would work nicely, or keeping it to all Italy.

Drove and did Comer See and Grindelwald end of August into September. Stayed a week in an apartment in Varenna. 2 days near Interlaken and 4 in Grindelwald. To this day one of our best vacations ever. Another trip - we stayed in Moneglia when visiting Cinque Terre. Starting in September some of the smaller boats no longer ran. The Uffizi was great!