I had a friend who managed a park and took her son with her (he was about 12 at the time, but she homeschooled the whole way through AND was a single mom). He'd kind of poke around with her occasionally, and then when she had things that she had to do, he would do his school work or play/investigate outside. I thought it was the perfect situation for them!
My neighbors are internet designers and they both stay home.
My mother was/is a real estate appraiser and the bulk of her time is at home. She does have to go out occasionally for the inspections, but the rest is from home. She made her own shedule. The classes to become one are not that intense or very long. Once she got things rolling for her own business, she made a very, very good living
My brother-in-law is a masage therapist. He works from home and also does very well and finds it very fulfilling.
Other people who I've seen that work from home and/or have the flexibility to make their own schedule and spend the bulk of their time with their children are: accountants, financial advisors, writers, designers, people who do things over the internet- like teach on-line courses, artists...