If it was my kid and they suffered harm because the cops went full retard on a doctor trying to treat her I’d sue those cops.
This behavior won't change until individual officers are held accountable for their inappropriate actions. Suing won't do anything but get you some money and make lawyers rich. The department will pay, and if they even try to do any real discipline to the deputy the union will fight it and likely get it overturned.
I understand why we set up the legal system and civil suits as a remedy for just taking your pound of flesh, but if the person doing the wrong is unaffected what's the incentive to change? How many times have we read stories of LEOs in bad or questionable shootings that had 5 or 5 previous complaints/lawsuits/payouts from the department.
We really need to look at adjusting the immunity we give people that we delegate the use of government force too. I fear, much like the the folks in cities that are tired of crime and lack of law enforcement and take matters into their own hands, we will start to see folks that are wronged by LEO's and denied justice by qualified immunity taking their pound of flesh directly.
I hope the young lady in question recovers fully, and the deputies involved have a serious talk with their makers about how they wade into situations.