Advice? For children's book??

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So several years back I took a creative writing class at college, and one of our assignments was to write a children's story/book. I came up with one for really young children that I feel has some potential, but I need some advice from some of you seasoned writers. First off, the book requires the person reading it to really interact with the kids and get them mimicking the actions. Not really sure how to convey that in the writing, since it is something I naturally do when I read it. Secondly, I have heard that most publishers prefer to pick their own illustrators to do the work for the books, but since it's a visual book, any ideas if I should send 'sample' pictures, to show them ideas of what's going on, rather than just words... and how good those sample pictures need to be?? And lastly... any suggestions for decent publishers of children's books who actually take submissions? Most I've seen don't seem to want unsolicited submissions, which is really frustrating! Thanks everyone!!