No, definitely not Moorcock. I don't think it was someone famous. And it was way more wholesome than any Moorcock I've ever read!

This is a stretch but is this the Swords Trilogy by Michael Moorcock? The Knight of Swords, The Queen of Swords the King of Swords. Each of these are small novellas which have been published in a single book as well. The main character is Corum, the eternal champion, who goes through quests that involve chasing a castle through dimensions.

No, although Shadow castle is on my TBR list! I don't think anyone comes from "outside" in this book. It's just the three siblings and they each have one main adventure. I think one sister has a romance with a shepherd, and one brother who is really into math and science goes to the moon(?).

Was it Shadow Castle by Marian Cockrell?

Not any of those, I've read them all! And most definitely not one of the Amber books -- I don't recall if it was marked as YA or adult, but it was suitable for younger readers in terms of not having any violent or racy content.

I can't remember any moving castles in the Dalemark books, off the top of my head, or that specific three-part structure.

And as for the Zelazny, Corwin's a main fixture in a lot if not all of the stories, but he has a huge passel of siblings, not just two. Is it possible you're remembering a couple of things combined?

The Guns of Avalon by Roger Zalazny, 1972. This one is number 2 in The Chronicles of Amber.

Summary: Corwin, a prince who has escaped from prison, attempts to regain his right to the throne of the perfect kingdom, known as Amber.

Read alike for Cygnet and the Firebird
Spells of Mortal Weaving by Esther M.Friesner, 1986. Part Chronicle of the twelve kingdons, series.

See if it's any of the books in the Dalemark Quartet series.

No. The royal children were the main characters. And the castle didn't fly around, it sort of teleported between two alternate locations.

Was it:

Howl's Moving Castle
by: Diana Wynne Jones

I think I read this in the early 90s but it could have been written earlier. It did have a somewhat old fashioned tone or style. It had three sections, each focusing on one of the three children of the king of a small country whose castle could move back and forth between the valley and the mountain top. At least I think those were the two locations -- I'm pretty sure the castle could only go between two specific places, not anywhere else. The king's daughter and two sons were grown up, not little kids, and I think one of the sons was named Colin or Corwin. It was NOT The Cygnet and the Firebird even though that also has three royal siblings and a moving castle.