I am not sure what you were charged with except that it is a domestic related misdemeanor. Only a class A misdemeanor is entitled to a jury trial. If you want a trial, any lower level offenses must be tried to a judge.
Customarily, on the eve of trial a DA will reduce a case like this to a B misdemeanor specifically to keep you from trying your misdemeanor case to a jury. It may sound unfair to you, but the DA has the right to do that, and, depending upon your judge, it may hamper your ability to prevail at trial.
That said, particularly if your wife is bothering you despite having secured a no contact order, there's no reason for you to jump at a disorderly conduct. A dis con is NOT a crime. But it does involve you taking a plea and it doesn't seal as deeply as a ACD, which is the better offer. In my experience, if you move the case towards trial, you'll ultimately be offered the ACD again if there's been no further trouble between you and your wife.
An ACD is hard to turn down. It does not involve a plea of guilty. All records of it are destroyed when it is sealed, exactly similar to what would happen if you were acquitted of all charges after trial without any of the risk. If you go all the way to trial and lose, in my experience, you will face at least some jail time.
As for your background check, it's illegal in NYS for an employer to ask about arrests that don't lead to convictions, unless they are government employers. So your pending case should not prevent you from getting a job.