I write and write and write, and then I edit it down to the parts that I think are amusing, or that help the storyline, or I'll write a notebook full of ideas of anecdotes or story points, and then I'll try and arrange them in a way that they would tell a semi-cohesive story.
I did have a child, and I was reading a lot of picture books to her, but at the same time writing a children's book was something that I'd been wanting to do for many years, pretty much since the start of my career.