A few weeks ago I left my 9-year-old daughter home alone for the first time. It did not go as planned.

That’s because I had no plan. My daughter was sick. My husband was out of town. And I needed to head to the drugstore—a five-minute walk away—to get some medicine for her. So I made sure my daughter knew where to find our rarely used landline phone, quizzed her on my cellphone number and instructed her not to open the front door for anyone. Then I left. Twenty minutes later I was back home. Both of us were a bit rattled by...