German trains- can you get off for a night at a stop along the way to your final destination?

probably not. it may be only good for the day of travel. do you have a ticket already? if so read the rules; it is that simple. you do not say what kind of ticket you have..sorry there are different kinds of tickets

I suspected as much. We will buy our ticket when we get to Frankfurt.

The answer to your question is "yes." I have done exactly that on several occasions when pre-purchasing a saver fare from DB. But you must schedule the stopover time so that your ticket indicates the trains you will be using for both trips.

I've just checked a random date in September and found a saver fare of €60 for two from Frankfurt to A'dam with an overnight stopover in D'dorf. Standard walk-up fares to A'dam will cost €170 - €200.

Are you doing that first leg to D'dorf right after arrival at FRA on an overnight flight? (In that case, pre-purchase might not be a good idea for a couple of reasons.)

Thank you all for the great information.

But buying the ticket to Amsterdam makes it international - and they are valid for 4 days.

That's true for Flex Price tickets but nor for the saver fare. Please look up the DB disussion board (let google translate for you):

Folgende unterschiedliche Bestimmungen zur "Fahrtunterbrechung Sparpreis Europa" sind zu beachten:
Belgien, Italien (via Österreich), Kroatien, *Niederlande, Österreich, Polen, Schweiz, Slowakei, Slowenien, Tschechien, Ungarn: Fahrtunterbrechungen sind, unter Einhaltung der Zugbindung, höchstens zweimal je Fahrtrichtung bis jeweils maximal unter 48 Stunden möglich.*

Four days is the 2017 standard completion time for international, full-fare, non-reserved, open train tickets along a specific route in Europe. (In previous years, it was two weeks and before that two months.) But this type of ticket is not widely purchased for Western Europe, where more trains require seat assignments and/or offer advance-purchase discounts with additional restrictions.

On a SparPreis (savings fare) ticket, you can specify a "stopover" of as much as 24 hours, maybe more. Use the Bahn website and play with the time leaving Frankfurt and the stopover time to get the layover you want (i.e., getting to Düsseldorf at a reasonaable time and not having to leave too early in the morning).