Yes, you should mention the fact that you are a single mother raising a child. You don't need to explain why you don't have a lot of extracurriculars - just mentioning that fact (somewhere in your essays) should be enough to tell the adcoms.
The hard truth though is that you're right as well - being a mother has little to do with your professional ability, and as a result having less time to develop leadership experiences in a professional/extracurricular context will hinder your chances, particularly at the higher ranked schools.
My hunch is that you'll likely get into Michigan, CMU and Ohio State. Kellogg, Booth and Wharton are stretches -- based on your professional experience alone you'll be a stretch, but not a long shot - you have enough of a chance that you should at least give these schools a shot.
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