You make some excellent points. As you demonstrate with the story about your three-year-old, adults often don't trust children enough - and when they do, it can pay off. How will children learn to trust if we don't show them trust?
Also, the paramount important of patience is often overlooked in child-rearing. Here you are, the most exhausted you've ever been in your life, and at the same time you are faced with the most difficult job in your life - child-rearing - with no previous training! This is far more challenging than any 9-5 job.
I sometimes resorted to giving myself a time-out when I felt my anger rising and wanted to prevent saying or doing something I would later regret. I only have to remember a few nasty remarks my mother made (still vivid in my mind, despite being decades in the past) to convince myself that this is worthwhile.