What happened to the red queen in chapters 10 and 11. In through the looking glass book

The red queen turns out to be Alice's kitty.

Explanation:

Through the looking glass is a book written by Lewis Carol. In this book, the central character 'Alice' goes through an imaginary world where everything is upside down. In chapter 10 and 11 the red queen is the part of the Chess game.

And Alice is really confused as to who the red queen really is. According to her she's her kitty. And she wonders whatever happened just now, was that her dream or someone else's dream.