THE TWO CASKETS: Inspiration for Alice In Wonderland?

          There was an animated movie from my childhood that resonated with me enough to haunt me into adulthood.  I can't remember the name of it, but it was about a young girl who falls down a well to a magical fairy country.  I was a big fan of Alice's Adventures In Wonderland, so it makes sense that this story with obvious similarities would appeal to me.  As an adult I've made numerous attempts over the years to find information about the animated movie with the girl who falls down the well, but without remembering the title I've had no luck.
          Then suddenly yesterday a direct link to it fell right into my lap.

Lang was sort of a Victorian-era Grimm, collecting folklore from all around the world
          I have several new editions of Andrew Lang's color-themed fairy books, and once in a while I read some, or flip through them, just because they're fascinating.  I picked up The Orange Fairy Book and randomly flipped to a story called The Two Caskets.  As soon as I started reading and noticed the first illustration, I gasped.  Girl down a well!
"That is an end of you she said"  "But she was wrong, for it was only the beginning"
          I realized immediately that it must have been the inspiration for that mysterious movie, and furthermore the similarities between The Two Caskets and Alice's Adventures In Wonderland struck me. 
          Consider the phrasing of the falling scene in each story.  Here's the line from The Two Caskets:

Down, down, down went the girl--it seemed as if the well must reach to the very middle of the earth.

          And here's the line from Alice's Adventures In Wonderland:

Down, down, down. Would the fall NEVER come to an end! `I wonder how many miles I've fallen by this time?' she said aloud. `I must be getting somewhere near the centre of the earth.

          In The Two Caskets, the girl discovers a beautiful and magical land where animals talk, and even inanimate things like fences and milk pails talk.  Alice also encountered lots of chatty things and animals.
          In The Two Caskets, the fairy country is referred to as the "under-world," and of course Carroll's original version of Alice's story was called Alice's Adventures Under Ground.
          Carroll's Through the Looking-Glass and What Alice Found There is bookended by scenes of Alice with her kitten, who is playing with a ball of yarn.  In The Two Caskets, a bunch of talking kitties follow the girl around with helpful advice, and one of the girl's main tasks involves two balls of yarn.

She found sitting round her a whole circle of cats
          And speaking of those balls of yarn, the task the girl is set to accomplish is to go down to the stream and wash a ball of black yarn until it turns white and wash a ball of white yarn until it turns black.  This totally reminds me of the kind of nonsensical demands the Queen of Hearts makes in Alice's story, such as painting white roses red.  And the way this task is accomplished is that when the girl fails to manage it on her own, some talking sparrows fly by and yell, "black to the east and white to the west!"  So she dips each ball of yarn respectively in the stream to each side and they magically turn the requested colors.  Is it too much to compare this kind of nonsense logic to the whole "one side of the mushroom will make you smaller and the other will make you taller" thing from Alice?

Take the black take the black cried the cats
          But which came first?  The oldest copyright in my edition of The Orange Fairy Book is 1906, yet it's a collection of traditional folktales from around the world, gleaned from numerous different sources, which seems to indicate the story itself is considerably older than 1906.  The particular source noted at the end of The Two Caskets is Thorpe's Yule-Tide Stories, but no date is given.
          Lewis Carroll wrote Alice's Adventures In Wonderland in 1865, but if the Two Caskets story had truly been around long enough to be considered folklore, then maybe he was heavily influenced by it.
          I'm not into reading annotated versions of classic stories because I don't like seeing things dissected, so this is probably not news to people who ARE into that sort of thing.  But it was an amazing and fascinating discovery to me.
          But I STILL don't know the name of that old animated movie!  Dammit.