Great that you gave her what she needed! It's NOT that a horse never needs firmness! It's that losing your cool, & getting mean and/or mad is murder on the relationship & ineffective.
Horses are hardwired to out-persist/frustrate predators, & when handlers get frustrated, the horse chalks one up for himself.
What actually changed here in OP's approach was that she DIDN'T get frustrated (yell, jab the horse in the mouth, etc) this time! Instead, she remained calm, didn't take the horse's antics personally, & gave the correction in the proper way & to the proper degree that the horse needed.