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'm was thinking the same way as Ken, passes are not always a good idea . But then I noticed some days are long and complicated, and a Flexi pass might work - but I wonder whether the tour duration is too long for that.

Don't forget, even with Eurail passes you still need to reserve on the French TGV trains and there is a "reservation" fee which can cost signficant money because it's actually a money making surcharge..

Does something happen in Macon, because no travel is shown there. Gimmelwald is a Rick Steves recommendation which few others have ever heard of, I was looking to see if Gengenbach appeared somewhere. But access to Gimmelwald is complicated so as a touring base I'm not sure.

Anyway, after Switzerland this all goes wrong. Colmar is 43 minutes on a direct regional express from Basel so why are you going as far north as Bacharach and turning back? The logical order is Switzerland, Colmar, Rothenburg, Bacharach, Trier, Luxembourg.

BUT if you were to buy point to point tickets the german fare system comes into play. DB will sell an international ticket from Lauterbrunnen to Breisach (german/french border point 15 miles from Colmar which have a local bus into city) for €49.99 and nothing to do at the swiss border - this covers local train to Interlaken, ICE fast train to Freiburg (with nothing to do at the swiss/german border) and local train to Breisach - an internal swiss tiicket from Lauterbrunnen to Basel border costs about the same!!! Comparison based on buying now for August.

The answer to the question about crossing borders is that it depends! The borders you will be crossing are mostly for railway operational purposes not passport control. The ironic thing is that as political changes have opened up freedom of travel, railway policies made it harder, 40 years ago more trains crossed borders! International tickets and passes are avaiable. The big point is that national and regional passes are valid to the last station shown in their conditions - two neighbouring passes may not cover the gap between them! A Eurail One Country pass for France covers to Basel, where you might be changing trains, but does NOT cover to Lausanne (another option from Macon) - you would need a Swiss ticket from Vallorbe and there may not be enough time to get out and buy it (so buy online)

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?