I am probably the demographic you are looking for. I freelance part-time, and I home educate a young child. However, I have a partner who is not financially abusive and I am not at risk of imminent divorce. If I was, there is absolutely no way I could do what I do. My partner's support, both financially, and emotionally is the only way this setup works. My partner also chips in with the education of several subjects - music, a second language etc - things I can't do well.
Regarding my work. I have a very niche career and I mainly work for American companies, so my hours mean I work in the evening when my partner has already finished for the day and can fully engage our kid. But there is times when there is overlap. Like today, for example. Something came in overnight that I had to deal with this morning. My DS sat next to me doing Reading Eggs and Math seeds on his laptop whilst I dealt with my stuff, which was fine for him, but for me, it was a nightmare trying to concentrate whilst his laptop was making so much noise! Luckily it's not often these things happen, but there's no way, as others have said, I could give 100% to work and my kid. Sorry, OP, I know this really isn't what you want to hear, but I have to be honest with you. The reality is much more stressful than the fantasy.
I second the advice to join Facebook at get onto the home groups. There is even a specific one for work from home jobs, with multiple posted daily. But please do have a long hard think about the realities you'll face, because it really isn't as simple as you think.