It is not clear to me what you are asking. You can't ethically threaten criminal prosecution to settle a civil matter. If it is criminal in nature, it is the DAs call whether to prosecute and not your decision.
Since you have an attorney, follow his or her advice!
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You question is hard to follow. It sounds like you are saying that you have evidence of a new crime committed by an opposing party in a family law case. It sounds like you listed at the beginning offenses for which this person has been previously convicted. Finally, it seem that you are asking whether you should use the evidence of a new crime to your advantage in the family law case alone or report it to the police, all him to be prosecuted, and use that new prosecution to your advantage in the family law case.
If all of that is correct, your lawyer cannot file charges against him unless your lawyer is a witness or a victim in the case. If you have information about a crime, you can report it to the police or not as you see fit as a citizen. You cannot threaten to report a crime to gain an advantage in a civil action (a family law case is a civil action).
As you have an attorney, that attorney would be in the best position to advise you further.