I can't say for sure, but if your ex has custody of your son they probably will take into account that he may not be a reliable witness against you in this regard (him being a minor anyway), though I can understand it must be painful for you regardless. It is a very sad thing when parents use their children against each other as weapons, and in itself can be classed as a form of abuse. If you are adament the allegations are false you could maybe bring this up in court. Bear in mind I am talking to you on the assumption you are an innocent man and she is the one in the wrong though, if she was or is telling the truth my opinion would differ and I would of course say that a father threatening the mother of his child like that in his presence is abusive.
It seems like one of those cases where, if there are no other witnesses, it may be a case of simply your word against hers, so if you are lucky the case may be dropped due to lack of evidence,