Dogs have tells too, and there's common ones that most dog owners will know:
- ears backed with tail tucked or quick wagging
- cowering / laying down (in a non-relaxed posture)
- deep growls and a leg spread defensive stance
And there's tells that occur far before the above. Dogs are domesticated animals (with millions of years of domestication, as opposed to cats), so comparing them in your head to a coyote is a false dichotomy from the get-go.
Your situation and GPs are very different. GP has specifically framed a dog that walked up to them off-leash. You are talking about having to potentially defend a child's life. There's a massive chasm between the two both legally and ethically.