Stay-at-home moms, do you actually "sit at home"?

I am a stay-at-home mom, and I have two kids. I have a "terrible two" who tears up the house like the Tasmanian Devil, and a newborn. I find that I am always "putting out fires" that my toddler makes, and I'm always trying to tend to my newborn. On top of that, I struggle to keep the house clean, whist trying to make sure that my toddler is stimulated and is learning something. My newborn doesn't sit in a baby swing and stare blissfully into space. Am I the only one who doesn't have a toddler who plays quietly in his room, and a newborn who just sits there as a blob, staring at his mobile? I'm also feeding, so it seems like I need to stop all my household chores almost every two hours to nurse. Why do folks think that I sit around and watch Dr. Phil?