I've noticed that recent replies on this post are responding to a question that was asked three years ago--so perhaps it's no longer relevant.
Anyway, FWIW, I wrote a parody of a very popular children's book once and was told by editors that it wasn't totally out of the question, but probably wouldn't be published because:
1. In order to sell, three and four year olds have to "get" the humor, and therefore must be familiar with the original. So many kids aren't even read to that it's a pretty high standard.
2. Yes, the target audience could be adults in which case your book would be a novelty item, not a true picture book. Most traditional pb editors wouldn't know how to fit it into their publishing program.
3. The original author (in the case of my particular story) was noted for being a bit prickly and probably wouldn't give permission. Yes, it isn't necessary to have permission in this kind of a case, but because she was much, much better known that I am, any publisher would think twice about offending her.
So for all those reasons, I gave up on the idea.