To write like a Mother Goose rhyme, you need to dismiss adult standards and just invent bouncy nonsense rhymes. Don't be afraid to use ungrammatical forms that may pop into your head. Dr. Seuss was very successful with nonsense phrases. The most popular children's books of the day are filled with old cliches. Children's poetry has only the rules that bring a desired response from children.
Rule books tend to stifle creativity rather than expanding it.
If you need rules to follow, make them up or use the oldest most tested ones. Your copy will be autographed by the poet upon request.