since it seems most of you didn't care for the details put on the previous chapters and this one, here let me spell it out for you:
1. The one Erica thought would go to the SR if she showed the necklace to was Ann (And so she DIDN'T show it to her), so she thought it would be fine if it's Klaus.
2. The necklace turned out to have a particular spell on it, which evoke desire and the East (Hafan) and North (Lucanrant) are especially vulnerable to this kind of spell (explained on ch 2). Klaus went to the SR because of this. Ann probably was only chasing after her brother.
3. If you read the notes on the last page and the chapter, you will know that the spell Phantasmal Maze has been cast on the Spring Palace, (it's not explained in the manga but the novel has the explanation) this made divides the palace into compartments. And those in one compartment cannot go into other compartment. So the rooms of the adults are probably in another compartment, while the Gate and Klaus/Ann room's is in one compartment. This is why Erica couldn't go to the adults for help, and the adults (if they noticed) couldn't go after the kids.
4. No matter who you are, your age, your gender, no one is omniscient nor omnipotent.
5. Also don't worry about Klaus, he will get his character development