There is not one specific train line. But you can use the Deutsche Bahn planner to look up train schedules. For Scotland/England, it's better to use the National Rail planner.

Do they accept the Eurail Global Pass?  That is what we are thinking of getting.

Yes, you can use the Eurail pass in almost all trains. More details on the individual country pages.

You'll need reservations for Eurostar from London to the continent (mandatory). You can book them via Eurail. From the Netherlands to Switzerland using day trains, reservations are optional and the best place to book those is via German railways (click on "Seat only”). Reservations (mostly optional) for trains in GB are free at any ticket office in GB.

More as 99% of all trains in these countries accept the pass. There are hundreds if not more raillines, the network is very, very dense and nearly everywhere you have a train at least every hour. AND congratulations-you are the wise guys. You have chosen those countries where travelling with a pass is a breeze, hardly any costly or hard to get extra REServations, as this seems to be the main complaint and puzzling thing on this forum.

In UK there is now 1 new low-cost line London-Edinburgh, named LuMO, that does not-the normal hourly LNCR trains do, but as for now you MUST reserve seats on thes etrains (free at stations).

In Swiss you can use almost all local raillines but NOT the mostly very expensive sections that go up those wonderful mountains. Do read carefully the country info-it lists it all. Most will give a discount though to passholders.