I don't think I know of any websites for children's books, specifically, especially of the scale of effort you're probably asking about. FunBrain at one point in time had a lot of stuff for the Diary of a Wimpy Kid books, since they were published there as a webcomic first, but I think it's more common for authors to have websites that have pages about their various books.
Dan Pilkey has a nice page for each Captain Underpants book with the cover, the blurb, a preview button for the first chapter, and a couple of little coloring book pages. That feels very doable to me.
But this post did remind me of my very favorite promotional material for any book ever: the interactive browser game (created by Failbetter Games) that preceded the publishing of Erin Morgenstern's The Night Circus. The original link is dead now, and probably a lot of the custom formatting along with it, but it does look like they're still hosting
a version of it on the interactive story-game-maker they came out with later on down the line. It's just such a fun world, and concept, and the visuals combined with the mysterious air of the Night Circus were pretty incredible.
I do feel like that sort of thing used to be more common for book and movie releases alike, in the old web days, with fun little extras and character blogs and even flash games, but I'm having a hard time remembering any of them now. Oh! Other than
Warrior Cats! (Not sure what age you've written the book for, but everybody loves a personality quiz. ;) )
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Hello Melonland! 
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