Munich to Salzburg to Vienna and back in one day?

Not advisable, unless your idea of a vacation is riding around on trains. On the other hand, blasting in and out of Salzburg for a day is a great idea. Use the Bayern ticket. Its good on regional trains after 9 am weekdays, all the way to Salzburg. 2 hours going and 2 hours coming back all for 26 euro for the 2 of you. Travel anytime on weekends.

The actual travel time of that itinerary would about 9 hours which doesn't leave much time for anything else.

Thank you both for your answers...can you give me an idea if it is possible to do Zugspitze and Neuschwanstein in the same day?

I think it could be done if you rented a car for the day. You need to make a reservation time at Neuschwanstein. I'd go there first, its about a 2 hour drive, then you have to walk UP HILL about 20 minutes to the castle. You need to be up there at your reservation time. You can also pay 5 euro (or so) and ride up in a horse-drawn carriage. You'll be out of the castle in about an hour. then walk back to the parking lot and move on. Its about 1 hour drive to Garmisch where you can catch the cogwheel train to the top, then come back down. Not sure of the timing. I think you need to be down by 5 pm. There is also a special "Moonlight Dinner" for about 100 euro pp, includes a 5 pm ride up the mountain, dinner, Bavarian entertainment. That is summer, so I don't know if that is going on in May which is a shoulder season. Its 1 hour drive back to Munich on the autobahn. You could also go the long way and stop in Oberammergau on the way back to Munich.
You could do both of these individually by train and bus on separate days, but it is too much trying to knock them both off in a day.

I didn't find Neuschwanstein especially desirable as it was just a show castle. Have you considered renting a car for a day or two and just driving south into the Southern Bavaria thru the Austrian Alps and back up to Salzburg? South of Munich is region that's easily to drive, and you can see so much more with a car.
And the mountain scenery of the Alps is absolutely breathtaking.

Hi, Not possible, assuming you want to be back in Munich by 2330. Even I doing zig zag train traveling would not suggest this. Keep in mind that Vienna to Munich, your last leg, on the RailJet train takes 4+ hrs, used to be 6 hrs. If you take a regional train, it is six hrs. You're going from Salzburg to Vienna, how many hrs there 3?

Is it necessary to stay the whole time in Munich?

We are going to base out of Munich for the time we are there as we rented a flat. Bavaria is the area my Hubby is most wanting to see. Thank you all again for your great advice. If there are things we should see in Munich, please let us know as this is our first trip and we are very excited.

Vienna is never a city that can be even appreciated for a few hours. 3-5 days maybe. Save a visit to Vienna for when you have much more time in days, not hours. Salzburg itself is worth at least an overnight if not 2 days.