Party of 4 - including kids? Ages?
Assuming you are all adults, the way to simplify your 4 major train journeys - and achieve a little convenience and flexibility - is to get two German Rail twin passes (flexi version) for 4 days. That would cover...
FRA to Nuremberg: Frankfurt airport (FRA) right? Or is Frankfurt proper a destination? If you are traveling to Nuremberg straight away after landing, then the rail pass is a big advantage since you can take ANY train or train sequence; a "best-price" saver fare would be train specific, and you could miss that train if you have a flight delay.
Nuremberg to Munich: Not such a major trip, and you could use a Bayern ticket, but a rail pass permits travel on high-speed trains and gets you there much faster.
Salzburg to Stuttgart: (high-speed train for long journey)
Stuttgart to FRA (high-speed train for long journey.)
You can pick up two German Rail twin passes for two at €288/couple (Springtime Special.)
(If you want to squeeze out some cheaper prices it might be possible with saver fares - you just have to check - but you then have set departure times with no changes, no leeway if you show up late, fees for any pre-arranged refunds/changes - and then more expensive tickets bought on the spot, at least 3 tickets per couple to fumble with and pre-purchase...)
The other tickets can be purchased locally once you are there.
Munich - Dachau - Munich using S-bahn + bus (MVV fare)
Munich - N'stein - Munich; Munich - Salzburg: Bayern Ticket
Salzburg - B'gaden - Salzburg: Bus 840 or possibly by train on Bayern Ticket (see this thread.)
OH YEAH, you're the group that intends to do all this over 7-8 days, right? I cannot see your new schedule clearly, but if that's still the case, then, this is still an overly-rushed trip, and the previous poster is probably correct that you do not have sufficient time in the cities. I think I've already advised you to eliminate the day trip to N'stein; it's nearly 5 hours on trains and buses + an hour's + walk all for a 30-minute tour, and you already have a day in the Alps scheduled as a day trip from Salzburg anyway. I will stick by that suggestion.
And I think you have kids. Well, depending on their ages the two GR passes I suggested may work; kids may or may be free with adult GRPs - check the DB German Rail pass for details.