I believe that a business that is best suited for a full time mom would be a transcriptionist. I think that this would be a good job because you can sit down at your house and type out the audio that you hear. You can keep it at a volume to where you can still hear your children. The only bad thing would be if you were a slow typer of if you had a massive time crunch before the project had to be complete.
I would say that working at creating passive income would be best for a busy mom - work at increasing it when you get a chance to, and while you're busy with your children or chores, you're still earning.