Likely if no lawyer is willing to pick it up there is not a liability case against the medical provider. For an injury case you need 2 things: liability and damages. It sounds like you have damages but not liability. In a medical malpractice case the mere fact that there was a bad outcome does not mean that the medical services providers were negligent; i.e., breached a duty of care owed to your son. So it is most likely that you have no case despite the brain trauma.
This is a gross over reaching by the cop he essentially gave you 2 tickets for the same occurrence in violation of NYS and Federal Constitutional protections. While there is no plea bargaining in NYC, I would certainly move to dismiss at trial as the Constitution still applies. You need to retain counsel and forget about your photo evidence because their does not need to be a posting - your defense lies in the law not in the facts. Don't go it alone retain counsel - it will save you money in...
YOU choose to get so drunk they had to toss you out. That you made another poor decision (driving while dunk) is not their fault it's yours. In other words, one thing (getting tossed from a bar) has nothing to do with another (driving drunk). You're just lucky you did not kill yourself or someone else. You should have called a cab.
Blowing a .054 is not a "non-violation." You have been charged with at least the infraction of driving while ability impaired and likely still charged with the crime of DWI. You can refuse the court orders if you do not mind a high bail being set and / or being remanded and if you are looking to take the case to trial. The prosecutor will not make you an offer unless you comply with the court's orders. So it all depends on how you want to handle your case.