Except for the fact that anyone can sue anyone else for pretty much any reason at all and, in that respect, yes, you can sue this lawyer who obtained information about you and your children and then provided this information to the person you filed a complaint against, the odds are pretty good that you do not have any legal action you can pursue against the lawyer that has merit or would have any chance of success. (sorry about that long confusing sentence)
Does this lawyer represent the man whom you filed the complaint against? Are your children central figures in the complaint that was filed?
Your social security number is private information and would normally not be disclosed under circumstances such as the one you describe. Your name, birth date, address and phone number are normally considered public information and could be shared with others, unless your complaint is of a confidential nature (ie, you are a rape victim and information about you is not being disclosed by the police). Your children's names are public information but, again, their identities might not be shared if they are crime victims. It would (generally) not be illegal to do so, however, and, if the attorney is working on a defense for the man, both he and the man will be entitled to all information gathered that will be used against this attorney's client.
Would you care to share more details about your situation, without revealing any personal data?