Make her come to you

While you could march into the cage yourself and simply drag the girl out by her hair, making her walk out herself will be better in terms off cementing who is the master and who is the ****. All it'll take is a little tact. And perhaps some intimidation.

"You know, I like to think of myself as a patient man. I don't fly off the handle or give unnecessary punishments. Everything I do is for a reason. By that same principle, I try not to do anything unnecessary. Like dirty my shoes by walking into a dirty dogs kennel when there legs work."

You snap your fingers and point down, right in front of you. Your stern expression make it clear your seriousness. Just as her angry expression makes it clear her thoughts of defiance." Did you just call me a-? " You snap your fingers with the same hand you were previously pointing down with, interrupting her.

You quickly pointed your finger back down, showing you had no intention of letting her defy you. By the same token she did not move, nor seem to have any intention of moving. The whole room is deathly quiet with only a bit of small talk from the people walking by outside sinking in. Garmen stood still, showing no sign he was going to intervene. He knew this girl was yours and yours alone to tame.

For a moment, you actually doubt your tactics. You begin pondering a change in tactics. Then again keeping on as is would show a strength in will, though it could take some time. This girl seemed to be rebellious though weak willed. Will she give in?