Italy and Switzerland in 11 Days for SIX People

Just one thing: I'm not sure the museums in Florence are still free on the first Sunday of the month in high season (although they used to be). I think it may now only be something like October to March. In any case, a free-entry day is a really bad time to go to one of the most popular museums. It's far better to choose a less-visited place that won't be overwhelmed with people taking advantage of the free day. Even then, you'll probably encounter more people than would otherwise be at that particular sight on a Sunday.

Hi. Others will chime in, but my first thought is that you aren't accounting for time it takes to change locations. For instance, it's significant travel (train, train, ferry) to get from Florence to Bellagio, then staying 1 night, and you say 'spend much of day in Como, train to Luzern. Suggest you think thru in more detail the timing / logistics. Look at the train schedules (trenitalia.com or trainline.com) and do some more detailed hour by hour, being sure to build in time for corralling 6 people to move in one direction, unplanned delays, bathroom stops, etc. etc. Have a great trip!

How many nights will you be there ten? Since you’re flying in and out of Malpensa why not stay in IT the whole time? Why take a bus or hire a driver to get from Malpensa airport to Milan’s central station when you can take a direct train from Malpensa to the central station (1h).
From Malpensa you could take a train to Venice that requires a change at Milan’s central station to the Venice Santa Lucia station (end of line meaning you get off with everyone else). Total time from Malpensa takes 4h and sleep in Venice for three nights.
From Venice take a direct train (no connections required) to Florence’s SM Novella station (2h 15m) and sleep there for four nights. This includes a day trip to Siena by bus (1h 15m).
From Florence’s SM Novella station take a direct train back to Milan’s central station (2h) and sleep in Milan for three nights and take a day trip to Varenna and Bellagio on Lake Como from Milan’s central station (1h 15m). Bellagio is a 15m ferry ride from Varenna.

"NEED TO LOOK UP SECRET PASSAGES TOUR"

Are you meaning the Vasari Corridor from the Uffizi across the river?

It does not look like an opening date has been set.

https://www.uffizi.it/en/news/all-is-ready-for-the-reopening-of-the-vasari-corridor

"Once the refurbishment works are over, the world-renowned Corridor designed by Vasari in the mid-1500s will be open to visitors again presumably from 2023."

Here is the ticketing page which is not active yet. There is a place where you can sign up for the Uffizi Newsletter, so I would do that and see if it opens by your travel time.

https://www.uffizi.it/en/corridoio-vasariano

DAY 7: JULY 4
Spend much of the day in Como, train to Lucerne

Unless you know something I do not, it looks like Varenna-Lucerne is a 2+ train changes over 5+ hrs.

You have to ferry from Bellagio to Varenna to begin the train journey. So from hotel to hotel you are likely traveling for 7-8 hrs.

If you cannot spend a 2nd night I would give consideration to skipping Lake Como. Add that day somewhere else and temper the brisk pace a bit.

My $0.02

I'd suggest skip the Cinque Terre day trip. The CT will be hot and very crowded. You are overall just spending too much time on trains, transiting, and not enough time being anywhere. It's exhausting to read it, even. I do like the suggestion to skip Switzerland this trip, ( as much as I love that country) , and go to Venice instead.
You have obviously done significant research, and do seem like a great planner. So let's research how much time it takes to get to check out, get to the train station, how much time actually on the trains, how long it takes to get to the next hotel and check in. Do that for every proposed location. You'll be amazed how much time all that eats up. (For example, you have yourself in Lake Como for only about 24 hours.)
Also, Viator is a third-party booking site. Contact the tour companies directly for better prices and communication.
Pls note that Europe will be very busy this year due to pent-up demand from the COVID years. Lodging is filling up fast.
Kudos for planning for a small group- that's no small feat.
Have a wonderful time!

For your train travel: suggest you use the web sight for "Man in Seat61" at https://www.seat61.com
Excellent resource for train travel anywhere. Lots of good ideas and tools to implement them.
Check out the Bernina Express -- a narrow gauge train with panoramic sightseeing cars run by the
Rhätische Bahn between Chur in Switzerland and Tirano in northern Italy

For LAKE COMO: stay in Varenna at the Albergo Milano www.varenna.net
and take the day ferry to Bellaigio