Confusion arises when readers can not orient themselves in the story. While complex storylines, lots of characters or multiple parallel events can lead to disorientation, they are not the source of it.
What you need are anchor points so the reader is never lost. The more rapid your pace or scene switching, the stronger they need to be. Cyn is right that rapid switches work in movies because you can put so many anchors into a shot - the lighting, colour scheme, weather, background and so on.
You could establish relatively simple but specific anchors and refer to them to make people understand where they are and with whom. In the mansion, maybe one unique feature about the room and one about the character, both to be mentioned in the first sentence after a scene switch.
Another trick used both in movies and written stories is to not jump between the scenes, but transition. Your scenes all happen within the same building, so you can "walk" your reader between them, like so:
(bla bla bla, scene in dining room)
All this commotion was barely hearable on the stairway outside, and even less so at its top, where the king was at the same moment meeting with the ambassador.
(bla, bla, scene between them)
On the same floor, just across the hallway and beyond the second door, the princess was still awake.
(bla bla, scene with princess)
Giving the reader a transition allows him to a) understand that the action is moving to another place and b) gives him orientation, in this case spacial.
As long as the reader knows where he is and with whom, he will not be lost.
One more word: Frantic action does not have to mean short and frantic writing. The beauty of the written word over movies is that you can disconnect the time it takes to read a scene and the time that actually passes in the scene. That goes both ways. Roger Zelazny has a brilliant piece in the first book of his Amber series, where after describing some battle action in detail for a few paragraphs, he continues with "and for hours, they died and they died". That is brilliant pacing because he already established enough detail, everything else would be repetition and it moves the story along. In other parts of the series he takes two or three pages to describe actions that take but a few seconds within the story. As a reader, that works, because all the details he describes advance the story or paint a better picture of some character.
You can easily do the same. Just because the action is fast doesn't mean you can't write enough words to let the reader keep his orientation in the story.