There are many parallels between the first and second books. Carroll seems to have turned many of the parts of Wonderland inside-out to create the Looking Glass world.
1) Alice follows the White Rabbit, whereas she scolds the Black Kitten
2) Alice upsets the Mouse, forgetting she is his size, and she is intimidated by the Flowers, who think she is a flower due to her size.
3) The Caucus Race, which goes in a circle, and the Train, which goes back and forth in somewhat straight lines, both suggest the foolishness of the masses.
4) Puppy and Crow both frighten Alice off, ending the scene.
5) Caterpillar changes form, just as White Queen does into the Sheep.
6) Mean Duchess & Humpty Dumpty both dominate Alice, Cat & HD sit high up
Cheshire cat is central character showing both ways, HD is central showing one stupid way
7) The Hare and Hatter both appear in the seventh chapter of both books.
8) Queen of Hearts & White Knight are opposites in their treatment of Alice.
9) Mock Turtle speaks of lessons, and the Red & White Queens test Alice.
11) Alice gets the upper hand and control. First escapes, now shakes.