Buddy, I don't mean to be harsh. No one would have an argument with his wife and then just get arrested. I argued with my wife probably 100 times already (and counting) and I never got arrested and I don't think I will.
So you hit your wife and you are going to say "that was my first time." Yeah, right.
Getting back to your question, You are only reading a small portion of the NY criminal procedures. You should check with your lawyer if your right is indeed being violated. Perhaps your prior court appearance already tolled the 90-day period. I am not a criminal lawyer and I just don't know. Entitlement to a speedy trail does not mean entitlement to speedy concludion of a trial.
Check with your lawyer, that is why you have a defense lawyer.