Train Travel - why is this so complicated??

On the first leg you can cut your costs significantly if you take the Flixbus from Milan to Luzern or Interlaken.
And then take the train to Murren. Just a note : If you get the Half Fare Card you can get an extra 50% off Super Saver Fares. Those tickets post 30 days in advance and sell out ; they are not flexible meaning the ticket that you buy is only good for the train and time you pick. But you save big time.

First of all, your question about train passes is the most commonly asked question on this Swiss forum. It gets even more complicated when you realize that your plans may change due to weather.

Also, your estimate of the half fare card looks incorrect. I think you looked up the yearly card for the citizens, whereas you might want the monthly one for about 120 CHF. See here:

https://www.myswissalps.com/swisshalffarecard/price

That said, you might also look seriously at the Berner Oberland Pass, and the 4 day pass is around 250 CHF and covers all transportation and boats South of Bern and Lucerne to Italy. (Tho just 50% off on Schilthorn.) When we used it, we separately bought the Milan to Domodossola ticket, then used the pass starting there. (But ask there about using the regular train, which is covered, and not the super express. They will tell you which.) But the advantage of this pass is that you can see a LOT using the cable cars and trains in the area.

For example, on Day 3 you have "up the Schilthorn". Ok, that might take 2.5 hrs. What are you going to do the rest of the day? Or, what if the peak is in the clouds? I'd suggest you take the cable cars/trains over to Mannlichen (Google image it) to take the Mannlichen to Kleine Scheidegg trail, the one I consider the best trail in all of Switzerland. Or ride the trains over to Pfingstegg where your kid could have fun on the Rodelbahn.

http://www.pfingstegg.ch/index.php/en/timetable-prices-4/toboggan

Or, take the cable car and bus over to Trummelbach Falls near Stechelberg. See

https://www.truemmelbachfaelle.ch/bildergalerie.html and click on the pictures.

With a pass, you can see a lot more in the short time you have. And personally, I'd lose the day in Bern to spend more time in Murren, Lauterbrunnen, Grindelwald, or Lucerne.

All these place names make more sense looking at this map:

http://ontheworldmap.com/switzerland/ski/jungfrau/jungfrau-summer-map.jpg

The Half fare Card comes in a tourist 30 day variety for 120 CHF per person, not the 185 CHF annual one that is is automatically renewed (and charged to your credit card) unless you cancel in writing.

You have 4 plus a 3-yo. Are they all adults, over 15?

The Swiss way is that trains are expensive, because it has the densest rail network in the world, and each station has at least 1 train every hour in each direction, even if there are only 3 people on the train. Plus Switzerland is one of the most expensive countries in the world because of an over valued currency.

I think a couple of your numbers are wrong. We're doing very similar trip to you in a few weeks coming from Milan and these are the numbers I'm getting:
Milan-Murren - Under 100 CHF (Around 10 euros from Milan to Domodossola, around 80 CHF from Domodossola to Murren)
Schilthorn - 82 (you must have only calculated one way?)

That puts your total more around 300 CHF full price.
The HFC is 120.
The Swiss Travel Pass includes everything you mentioned except Almendhubel and the leg from Milan to Domodossola (around 10 euros)

If you do the HFC, you'd probably save around 40ish CHF per adult, plus the free child. That's cheaper than the STP, except that the STP allows you to just get on/off trains without buying tickets (convenience) but would be an extra 250ish CHF for your group.

Also, if you know your dates in and out, you can purchase the Saver Day Pass in conjunction with the HFC for 29CHF for a full day, so you can turn that Milan-Murren into potentially around 40ish CHF (11 euros from Milan-Domodossola) and then 29CHF from there to Murren. Note, you have to buy these 30 days out to get the best deal.

https://www.sbb.ch/en/travelcards-and-tickets/tickets-for-switzerland/1-day-travelpass/saver-day-pass.html

Swiss train tickets are expensive becaus everything in Switzerland is expensive. You have to accept that if you are going to travel there. We have been there for two-week visits several times , but not for ten years because of the expense. Returning this summer because I am celebrating a big birthday.

Think of all the engineering that goes into their train system, particularly through the Alps. It is one of the most expensive systems in the world to build. But it enables people to reach some beautiful places, like Mürren.

To address your question, I see you have figured at least one price incorrectly. Both Trenitalia and SBB sell discount d advance tickets for the cross-border journey. Only SBB will get younthe whole way.

Milano Centrale to Mürren can be purchased for 64 CHF on SBB if you buy far enough in advance. ( I was looking at 8 August).

If you buy from Trenitalia, you could get a Mini fare of 29€ as far as Spiez. Then buy from Spiez to Mürren from SBB for 30,20 CHF.

As for the Schilthorn, are you riding up and hiking down? The price you found is just one way. Double it if you want to ride back down. It is a pretty rugged hike.

As a general rule, a Half Fare Card ( 120 CHF for a visitor's 30-day card) will benefit people who want to ride up the Jungfrau, as it covers a full 50%. Since you are not doing that, you may not get sufficient benefit from the card to make it worth the cost.

A Swiss Pass, whether 4-day Flex or other, will fully cover the whole Schilthorn trip. But if you are only riding one way, it will not be worth covering with a pass unless you plan other train travel that same day.

Here is one way to look at it: A 4-day Flex Pass costs 310 so to make it worthwhile, your four days of use must average 77 CHF each. If you get those advance discount tickets for the trip from Milan to Mürren, the only day you have planned that will meet that threshold is the Schilthorn trip, IF you plan to ride it both ways. If you are riding only one way, you do not have a single say of travel that would be worth covering with a Flex Pass.

And if you do not buy far enough ahead to get the discounted ticket from Milan to Mürren, the regular fare for comparison purposes is 109 CHF on SBB, or 59€ plus 30 CHF if you buy from Trenitalia as far as Spiez, and SBB from there.

So I do not see any benefit to buying a pass for you.

Yeah Switzerland is expensive. You will notice even the price of all goods like coffee is double of what it costs in neighboring countries

The Swiss train system and trains work. They are on time to the minute, frequent, clean and comfortable. Swiss workers are paid decent wages.
https://en.wiktionary.org/wiki/you_get_what_you_pay_for

In you are coming from France, delays may happen on the French side because of work actions: https://www.swissinfo.ch/eng/business/train-unions_french-strike-affects-swiss-rail-connections/44018548

https://lenews.ch/2017/01/26/swiss-fact-work-days-lost-to-strikes-in-switzerland-close-to-one-ninth-of-neighbouring-countries/

Swiss travel Pass for 4 days will be the most convenient, it will save time, and will enable you to jump on trains, boats, funiculars without a second thought. It even covers a trip to Schilthorn this year. You could go up to Schilthorn, Murren, Wengen multiple times during your stay in Bernese Oberland to do hikes, or if weather isn't great on one day, you could go again to the same place on a different day. Almendhubel isn't covered but I believe it is discounted with the pass.
Buy the ticket from Milan to Domodossola ( the last Italian stop ), and use the Swiss pass from the border. The last day ( day 5 ?) you just have to buy a ticket to Zurich.

Don't underestimate the number of trains/funiculars/cable cars/ etc. that you may need to take; and I am sure any point to point tickets will end up costing more then a pass.

I am normally in favor of using a Swiss Pass, but they only have two days in the Berner Oberland before moving on, so there will not be many opportunities for trains, lifts, and boats to cover with a pass.

The cost of the travel plans they have listed, using Point-to Point tickets, is 229 CHF if they get the good advance purchase fare of 64 CHF on the journey from Milan to Mürren. I found this fare for a date in early July when they will be there. If for some reason they do not get that fare ( allotted discount tickets sold out) they will pay more, but no more than 109 CHF, which is the "regular" online price for the cross-border journey. Then the total,for tickets will be 274 CHF, still lower than the 310 CHF they would each pay for a 4-day Flex.

IFF they miss out on the discount so they pay 109 CHF to get to Mürren from Milan, AND they are riding the Schilthornbahn roundtrip instead of one way, that adds some 45+ CHF to the 274, in which case they would break even with a Flex Pass. And they would have the convenience of just boarding trains without purchasing tickets, which is worth quite a bit

Thank you, everyone, for your advice. I am wading through it. One question I have is for folks who are saying that it is possible to get a train from Milan to Domodossola for 10 euros. Every time I check for July 7th, the cheapest I can find is 47.50. https://www.lefrecce.it/B2CWeb/search.do?parameter=searchOutputViewer&cFID=AXiyuOFze3rC

Am I looking in the wrong place? What am I missing?

Also, I really appreciated folks' advice on what to do in the region. I don't know Switzerland well - it's our first trip there. Based on the suggestions people made, it seems like a Four Day Flex Saver Pass might make the most sense so we can do more while we are there. Do you all have any other suggestions for what we should be doing while we are there? We are staying in Murren. I like the idea of the Panorama Trail and the Blumental Panorama Trail. I wonder if there are others that are suitable for a young child (who may walk some, ride in a pack other times)?

Thank you everyone.

47.50 euros sounds like your total for 4 people. If I look on Trenitalia for the InterCity train departing Milan at 8:23, for instance (which will runs all the way to Geneva), the cost for 1 person in 2nd class is offered for 9.90 euros Super Economy rate, up to a maximum of 22 euros Base rate for one adult in 2nd Class. Those costs are similar on every departure that morning, including EuroCity departures at 11:23 and 12:23, which are also long-distance trains with fewer connections.

FYI, on our updated Italy cost map, we show the rate as $20 (for future readers making similar comparisons).

Yes, that's absolutely it. Thank you.