Castle alternative to Neuschwanstein??

If you are going from Hallstatt to Munich, will you be stopping in Salzburg? Hohensalzburg Fortress, overlooking Salzburg, is an authentic castle.

Closer to Munich, one of Ludwig's palaces, Herrenchiemsee, is on your way, but it is only a palace (a poor replica of Versailles), not a real castle.

The Burg at Burghausen is a real castle, but it takes as long to get to as Neuschwanstein.

Karlstejn near Prague, which is real, and one of Europes most beautiful and important castles (it was built to keep the Imperial Regalia of the Holy Roman Empire).

Well Neuschwanstein is not the only castle in Europe, to be fair it's not actually a real castle, but a 19th century romantic set piece, build by a mad opera fan. It's beautifull and enjoyable, but quite kitsch on the inside and by no mean representative of a proper medieval castle.
An alternative could be Karlstejn Castle near Prague, which has retained some of it's medieval look: https://en.wikipedia.org/wiki/Karl%C5%A1tejn

If the weather is beautiful a day at Herrenchiemsee may be very entertaining. First you board an ordinary train, at Prien you change to a local train line (in summer often with steam locos), than you switch to a ferry, then you either have to walk in woods or take an horse cart to finally get to the palace. Children would find the whole procedure very entertaining, I do not know your daughters.

Most of the entertainment in Ludwig's castles (Neuschwanstein, Herrenchiemsee, Linderhof) is the sheer madness of building castles in 19th century when they were not really needed and after outdated models. Neuschwanstein is probably unique in being a piece of Disney phantasy about one century before Disney.

With the route you are taking, Herrenchiemsee would be the easiest and the classiest to get to. There should be a stop on one of the trains from Salzburg to Munich. The island location is nice. The palace was inspired by Versailles but is on a smaller scale and is not the vulgar display of wretched excess that Versailles is. Lee forgets that Neuschwanstein is pure theater, so much so that my German relatives spit when they say the word. It might be hard to plan traveling by train but if you are there at the right time and plan it right, in summer there are concerts and you can Mozart in the hall of mirrors by the light of 10,000 candles but that's a bit of a trick to plan.

As mentioned above, Neuschwanstein, though located in a pretty place to be sure, is not really a castle. Rather, it's the palatial residence built by an unstable young late-19th-century king who occupied the place just a short time before he was mysteriously found floating face-down in a lake. There are spectacular palaces with more significant history, easier access, and much less crowded with tourists, in Munich proper. Examples are the Residenz, Nymphenburg and Schleißheim. Residenz and Nymphenburg are both accessible from anywhere in Munich via public transit. The relatively-untouristed Schleißheim palaces are a short ride on the S1 from the city center, to the Oberschleißheim stop, then a ten-minute walk.

Some intact castle alternatives that may or may not be more convenient include Burg Trausnitz above Landshut (about 1hr-90 mintues from Munich), Burg zu Burghausen (about the same distance from Munich), Burg Hohenwerfen south of Salzburg and Burg Hohensalzburg within Salzburg. There's hundreds of castle ruins throughout Germany and Austria.

The in-city castles in Prague and Cesky Krumlov are popular sites on the tourist route. I'd also include one of the Munich options, for comparison.

This is exactly what I was looking for - so many wonderful options! Thank you so much to everyone for your suggestions and advice. Much appreciated.