1-Month Italy, Paris? & Switzerland Itinerary help?

It is quite a lot of backtracking, but I assume that is because of your daugther's schedule? In that case the only comment I have is that it is not necessary to fly from Paris to Switzerland, there are direct TGVs from Paris to several Swiss cities and they are often the fastest option.

I would first sugggest getting some guidebooks as you are all over the place.

A few notes. To get from Lugano to Varenna you eight have to take the train to Como and then a long ferry to Varenna or the train from Lugano to Milan and then another train up to Varenna.

I would do this completely differently utlilizing the same destinations.

Let's forget Paris for a moment. My itinerary would look like this:

Lugano
Bern, Switzerland (train)
Lucerne, Switzerland (train)
Lauterbrunnen Valley, Swtizerland (train)
Brig/Zermatt, Switzerland (train)
Chur, Switzerland(Glacier Exprress)
Tirano, Switzerland(Bernina Express) to Varenna on Lake Como .
To Naples/Sorrento (train)
Puglia
Lugano

All of Switzerland can and should be done by train. The Glacier Express and Bernina Express are spectacular train rides thought the Alps. The trains from Lucerne to Lauterbrunnen and then to either Brig/Zermatt also offer wonderful scenery. You don't need cars anywhere in Switzerland unless you are going to the smallest of towns which for a short visit is probably not necessary. The train system is excellent. The Glacier Express and Bernina Express are sightseeing trains that need to be reserved months in advance.

No need to stay in Tirano after the Bernina Express.. The train from there to Varenna on Lake Como is just about an hour or so. You will have to change train stations but they are next to each other and not very big.

If you must see Paris, my suggestion is to do it between Bern and Zurich. Yes it is backtracking but it's less than what you had planned. Or, if you don't have your flights yet, after picking up your daughter, travel to Paris with her and fly home from there. (Fly into Milan and home from Paris.)

Your daughter must be attending The American School in Switzerland. My daughter spent a year there when I worked in Saudi Arabia in the 80s. Lugano is beautiful.

Why are you going to Bari, that has never been on my travel list?

Switzerland, we loved Interlakken.

Before buying a train pass, look into the half fare card. It might be cheaper to buy the half fare card and use it instead of a train pass.

https://www.sbb.ch/en/leisure-holidays/travel-in-switzerland/international-guests/swiss-halffare-card.html

I feel like you are kind of all over the place. Is there a reason you are going to the southern part of Italy when your start and end point is Switzerland? I think there is a lot to see that is a closer loop if you will. Your already spending 9 nights in Switzerland (I think you could shave some off of this), maybe just add on the Veneto, the Italian Lakes and places like the Dolomites? You could also do some of the very western section of Austria (Tirol) and southern Germany (Munich and the Black Forest). Any combination of these would make a good loop trip.