Soliciting help with choice of Rail Passes

One of my blind spots is how the European Rail system handles a
traveler moving across borders with without all advanced passes. Do
some trains travel "non-stop" across borders or do we have time to
jump out and buy the next ticket/pass before jumping back on a train?

You can travel on multiple tickets without having to get off the train. Eg. If you have a pass that covers A - B and ticket that covers B - C you can just stay on the train from A to C. Trains work on "proof of payment". You need to be able to show at all time that you have paid for being on that train. It does not matter wether that is a ticket, a pass, or a combination of tickets and passes...

For example on how to combine tickets: Suppose you have a Swiss Travel Pass and are travelling from Gimmelwald to Kuppenheim. All you would need is to add a ticket from Basel Bad bf. to Kuppenheim. You could buy that ticket online, or at a convenient time at eg. the Lauterbrunnen ticket office. Then you could just take the Interlaken to Baden Baden train, and stay on board as the train crosses in to Germany.

Regarding wether trains go non stop, or you need to change trains at a border station: You can find all that out using the usual train trip planners. But you should always try to have all parts already covered by tickets when you set out, in order not to have to waste time at a border.

As to your actual travel plans:
Local trains in France do not need to be booked in advance. TGVs do, and booking TGV services with an Eurail Pass is complicated. I would not bother in your case with a pass for France.
For Switzerland the Half Fare Card or the Swiss Travel Pass may be a good option.
Maybe for Germany the "Deutschland Ticket" would be of use.

Given the number of rail trips you'll be taking, it would take some time to work out the most cost effective rail pass or ticket options. Some of the trains you'll be using may be premium trains which require seat reservations, and those are not included in the cost of the rail passes. I haven't checked but the children may be able to travel for free on some trains.

You might find it helpful to have a look at this website - https://www.seat61.com/ .

It would be an interesting experiment to submit this question to ChatGPT or other AI.

I am coming to the forum with set hotel reservations & nearly set itinerary,

That's unfortunate. The assistance you need with trains involves more than just ticketing advice. Your choice of destinations and the sequencing you have in mind for the final two weeks in Germany will involve some very undesirable logistics that are simply not fixable as they stand right now.

A bit of additional information regarding travel to Gimmelwald (I'm assuming you don't mean Grindelwald).....

Access is reasonably straightforward. When you arrive at Lauterbrunnen station, transfer to the Post Bus (it will probably be waiting) and take the short ride to Stechelberg. Board the Schilthornbahn cable car and you'll be in Gimmelwald in a few minutes.

Where are you planning to stay in Gimmelwald?

Thank you all who responded:

JPHBucks, I did not leverage Ai, but…
Ken I reached out to The Man in Seat 61 and he suggested that I at least price out a Global Eurail because, as you guessed, kids travel free with adults, and a couple other advantages he mentioned which I reference below.

me.crewe, The tour duration is just under a month and so we could do the Eurail “7 day 1 month flexi” or the “10 day 2 month flexi” options. Unfortunately there isn’t an 8 or 9 day option which would actually best fit our itinerary (Eurail pass above Lauterbrunnen is usually discounted (only 25%) and yet not counted as a day of travel on Eurail pass)
As yes Russ, as I shared, it’s unfortunate that the 2nd half of the itinerary has some significant backtracking; any extra travel cost is absorbed in a Eurail pass but obviously not the extra hours of travel. Also the Eurail pass would cover the potential gaps in state or national passes. Thank you me.crewe for pointing that out as well as the surprisingly relatively inexpensive DB travel from Lauterbrunnen to France and Germany. I priced out much of my trip on their site for comparisons.

Wengen, Thank you for explaining the process of crossing borders and the concept of “proof of purchase”. Very Helpful.
And also the main potential Eurail drawback: the process AND cost of booking TGV seat reservations, since most our travel in France will leverage these.
Man in Seat 61 website has much train travel info that he might have a manageable solution.

Thanks to all, and while Man-In-Seat-61 has me leaning toward a flexi Eurail l am open to further input. Appreciate you guys!