Since the majority of the school day is usually devoted to language arts and math, you can feel good that any teaching you are doing in any other subject is probably more than they would be getting in public school. The backyard and the kitchen are probably the best science classrooms. Learning to interact with others across generations is social studies. Remember, a textbook and worksheet is not a requirement for learning! And give yourself double points for doing anything ever in art or music!
It's hard to prevent them from learning. Kids are naturally curious. In fact I am sure there is a direct correlation to the curiousness of your children to the messes they are responsible for. (I don't know if that's true, but it's a comforting thought, isn't it?)
You are teaching them valuable life skills. If you made your child go back and brush their teeth (this time with toothpaste) or stop to say thank you to the neighbor who gave them a compliment, or pray before lunch, you're teaching them! Don't sell yourself short. These important life skills are part of the well-rounded education that you're giving them!
They can always learn it when they're older. I have a confession to make. I never learned the whole pint/cup/quart thing. Or gallon. Maybe I missed that day. But you know what. I turned out ok. And I'm learning it. Two cups in a pint, right? Though I still think liters and milliliters make SO much more sense. And everyone knows how much 2 liters is. But I'll save that soapbox for another day. My point is that in reality some things might get missed. But that's okay. Anything that can be learned at 6 can also be learned at 16 or even 26!
In all seriousness, taking on the education of your children is no small task, but just realize that you don't have to be perfect. I love Psalm 25. I call it the teacher Psalm because the Psalmist uses verbs like teach, show, guide, and instruct to describe God's actions. And really, isn't God the ultimate teacher? It's amazing to think that God understands how to solve algebraic equations, diagram a sentence, and conjugate Spanish verbs. He also knows about learning styles, teaching methods and techniques . And He knows how to work through us to educate and care for our kids. He gives us the patience and grace and perseverance to take on this amazing challenge. And if God is on our side, we're gonna be just fine. Even if our kids don't know who Pablo Picasso is.