Wonderland and the world of Through the Looking-Glass are the same world, just different sections of it.
All the places introduced are aspects of Wonderland itself, just in different areas. Maybe mirrors in that world are used as Cool Gates? Alice only got to visit one kingdom in Wonderland.
Since the Wonderland she met had a Queen of Hearts and a King of Hearts, shouldn't this world also have the Kings and Queens of Spades, Clubs and Diamonds as well? Maybe they have their own kingdoms in Wonderland. Alice has negligent parents and/or is a wealthy orphan.
Now of course in real life, Alice Liddell's parents both lived into her adulthood, and Carroll probably wasn't commenting on their attentiveness as to their children or lack thereof. Still, it seems strange that the fictional Alice's parents are never once mentioned, even though other people from her everyday life (her sister, her brother, her nurse, and her governess) do get mentions here and there. In both books, she also seems strangely unconcerned with whether she ever gets home again or not, and the only one she imagines missing her is her cat.Pat the Gardener is an Irish hare
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To contrast against the English rabbit..