How do I go about making a second edition?

I published a children's book with Author House a few years ago and it came out completely bad. The format of the book was wrong as well as the style illustrations and more.

I did pay for the copyright of the book and have been thinking about making a second edition (I think that's whay it's called?) where I can make edits to the story, and completely change all the illustrations.

What I want to know is:

Can I make a second edition with a new publisher? I know I'd have to more than likely ask the publisher themselves.

How much change can be made for it to be considered a second edition and not something else? The format they made was printed to look like a young child's picture book, when it should have been a formatted to look like book book...if that makes sense. It was aimed at kids 8-10.

These are the main questions I have, but if anyone has any advice or things I should consider please let me know!