3 full days in Munich

I just visited Munich and from there, including transit time 45 minutes each way you should plan on 4-5 hours--according to my tracker I walked 8 miles that day, it's quite spread out and it's all worth seeing. I can't see how you could also fit in 2 hours total on the train to Nuremberg. I did that as a separate day trip and started with the Dokumentationszentrum museum then out to the rally grounds before taking the tram back and exploring the lovely old town for the rest of the day--lots to see there. I chose Nuremberg over Neuschwanstein and it was one of my most enjoyed day trips. With 3 days in Munich I'd do a full day in Nuremberg, 1/2 day to Dachau and the rest depends on your taste-Nymphenburg Palace was easy to get to on tram and good for 3-4 hours, plenty of museums in town, the English Garden, Residenz, etc. If you have Rick's book it details how to do Neuschwanstein if you choose to go.

You only have three days in Munich and you want to go out of the city? You can't begin to see Munich itself in three days. Dachau is a day trip by itself. Nuremberg is another 2-3 days just for the city center. Neuschwanstein Castle is another full day with the drive and lines. Slow down and enjoy the city instead of just running from place to place.

If you don't want to spend all that time driving down to Neuschwanstein Castle jump on a tram and visit Schloss Nymphenberg. It was the place where royal visitors stayed until granted an audience at Hohenschwangau (which is the castle Ludwig lived in; Neuschwanstein was just for show and is unfinished.)

I second what KGC stated. Munich is an absolute delight and requires 3 days to absorb everything. I found Neuschwanstein to magical at night when the tourists were gone, but certainly would not devote a day to travel to/from when Munich has so much to offer.

Have you thought about taking a quick 50 minute train ride from Munich to Andechs Monastery? When in Herrsching take a stunning walk in the countryside up to Andechs Monastery where you can grab a beer, sample great food and see some stunning views.

I don't know transportation details from Dachau to Nuremburg. However, I can't see doing both in the same day.

On the other hand, you could definitely do Dachau + Munich's Nazi Documentation Center in one day (I would visit Dachau first). I did this in May 2018. The Doc. Center has a broader focus, so I didn't feel I was seeing duplicative material.

In the courtyard outside the Doc. Center is a plaque showing where the Nazi buildings were in this neighborhood in 1930s-1945. Within eyesight is the building that housed Hitler's office. Above the door one can still see small squares where the Nazi eagle was once hammered into the stone. My understanding is that the 1938 Munich agreement (Neville Chamberlain, French representative, Hitler) was signed in this building.

You can visit Dachau in half a day. It is only about half hour railway ride from Munich. I guess you mean Dachau concentration camp site because there a Dachau town also with nice old town (Altstadt) https://www.youtube.com/watch?v=e6PBdSm9r38&t=1s
If this is your first visit to Munich I would not recommend Nurenberg because it is far away, and you can't even scratch Munich alone in 4-5 days. There are so many interesting places in Munich that leaving it if you have only 3 days is not reasonable. Neuschwanstein Castle is not among these places, I visited it a few years ago and it is nice from outside but too touristy and there are long lines always, I had a feeling I was in a supermarket and that every one just waits for me to go through it ASAP and make space for the next group. And also interior is partly unfinished, you have much more to see in say Residence, Nymphenburg etc. See this and decide for yourself whether you can visit even half of it in 3 days. https://www.youtube.com/watch?v=32bz2l1q9oY&t=1s