Is the Swiss flexxi pass my best choice?

Hello,
My wife, daughter (9yo), and I are traveling to Europe this summer. One of the jewels in our trip is an 8 day train trip throughSwitzerland. At first I thought weneeded an 8 day Swiss pass, but now I think differently. Here is our itinerary:
Arrive in Luzern from Rothenburg via Frankfurt.
Day 1-boat & train, Luzern to Mt.Pilates & return (no cable car)
Day 2-train, Luzern to Interlaken
Day 3-train, Interlaken to Jungfrau, return
Day 4-train to Zermatt
Day 5-train, Zermatt to Matterhorn (Gornergrat),return
Day 6-train, Zermatt to Chur (next day inChur too)
Day 8-train, Chur to Tirano
Questions:
I think I need a 4 day Swiss flexi pass to cover 1- Luzern to Interlaken, 2- Interlaken to Zermatt, 3- Zermatt to Chur and4- Chur to Tirano. Is that correct?
I think the side trips to Alpnachstad & Mt Pilatus, Jungfrau, and Gornergrat (Matterhorn) are discounted with a Swissflexi pass, but not covered by the flexi pass. Is that correct?
I also think that a Swiss flexi pass is financially better for our trip (gives the best discounts in Switzerland) than a Eurail pass for 7 countries. Is that correct?
Thanks for your help.
Tom

Hello Tom, and welcome to the forum! I think 4 day Swiss Saver Flexi Pass would be the best choice indeed. It may be better though to use the 1st free travel day for your inbound trip from the German border to Lucerne, instead of for day 2. That's because the Swiss Saver Flexi Pass only becomes valid with/after the first free travel day. If you start using it on day 2, that means you won't get any discounts on the Pilatus and boat trip you want to make on day 1. Other free travel days should be used for Interlaken-Zermatt, Zermatt-Chur and Chur-Tirano. Lucerne-Interlaken on day 2 isn't that long and expensive, so you don't need a free travel day for that trip.

Pilatus, Jungfrau and Gornergrat are discounted indeed, whether or not you use a free travel day. All details, including a downloadable map showing the area of validity and purchase options, can be found at the Swiss Flexi Pass page.

Thanks Annika. I really appreciate your help with this. Thanks also for this web site and all the services, it is a great help. I am really looking forward to Switzerland. It will indeed be the jewel of our Europe trip.

Glad I could help, Tom. Enjoy your trip to Europe!