Working from home must have been the holy grail for my single parent community. I've studied the prospects for over twenty years. The problem with successful home businesses, is that you have to be constantly drumming up new business as you try and meet your current commitments. Business startups take at least as much energy as a new baby.
I think the most efficient option for a single parent is a job with regular hours with a large employer, like IBM or a government office. That way, you have benefits and set hours. Hence, more time with your children.
BUT if you are committed to working from home, I'll tell you what I learned from those who were successful. Don't buy in to Tupperware or those other multi-level marketing schemes. Your take-home is not worth the effort. You may have to run several businesses on the side, say, a cleaning service and something else. I hope you are comfortable selling yourself. All the time. To family, friends and strangers.
The coolest at-home job I found was graphic artist. She established her reputation first, in New York. Ever after she worked from her acreage in the country, frequently reminding the big publishers of her existence by mailing out postcards of her work. She said Fed-Ex was her best friend.
By the way, the religious right is BIG on home-based businesses. You might find resources from them.
http://www.visionforumministries.org/events/eb/001/schedule.aspx