I think you’re wrong, but you may not be.
When I got able to, I called my wife from the hospital, and she went to the police station that same day. The next day when I walked in, the chief looked up from his desk and when he saw me he said, G.D.!, I hope you aint as mad at me today as your wife was yesterday!!
What constitutes necessity is legally defined and would be a matter for the jury to decide in a trial, if it got to that, or a judge in a traffic case, since those don't have jury trials. I think that your case would definitely constitute a legally-recognized necessity. The NFL player's case would be questionable, because he was not personally facing an emergency, and there are many occasions in life when we want to be somewhere quickly, but life and property are not in danger if we are not. It would be too large an exception.
That said, the Dallas cop was a jerk, and they were right to reassign him.
Sounds like you have a helluva wife. Thank God there are still jurisdictions where you can yell at the cops without being thrown in the slammer on some phony charge.