Lady Friday by Garth Nix

From the publisher (source: The Internet Book List):
Arthur Penhaligon's adventures in the House get ever more perilous as the week unfolds. On the fifth day, there was fear...

Four of the seven Trustees have been defeated and their Keys taken, but for Arthur, the week is still getting worse. Suzy Blue and Fred Initial Numbers Gold have been captured by the Piper, and his New Nithling army still controls most of the Great Maze. Superior Saturday is causing trouble wherever she can, including turning off all the elevators in the House and blocking the Front Door.

Arthur can't even find out what is happening back home. All he knows is that Leaf isn't on earth any more. She's missing and so are hundreds of other people who were transferred from regular hospitals to a private institution run by a 'Doctor Friday'. From there they have been taken somewhere else in the Secondary Realms, for Lady Friday's own horrible purposes.

Amid all this trouble, Arthur's mother is also missing, and he must weigh up an offer from Lady Friday that is either a cunning trap for the Rightful Heir or a golden opportunity he must seize � before Superior Saturday or the Piper beats him to it.

This book is part of the "The Keys to the Kingdom" series.
Here are some other books from this series: