I'm thinking of letting my niece out of her cage at least once a day.
Wait what? Did you say letting her out of the cage?
It makes it possible for her to spend at least some time outside of the cage.
You should treat your niece like a human being. It's not right to put people inside cages because they are not animals. What you are doing is very harmful to your niece.
I need to punish her for not doing what I want.
Just because she's not behaving, doesn't mean that she deserves to be crated up like an animal. She is a human and deserves to be treated like one, this can be very traumatizing. You should treat her with respect and love and stop disciplining her in such dangerous manners.