Legally in my state you do not have a right to know about his relationships, you are no longer married, however you do have a right to know that your xchildren are safe, but without her name and date of birth you will not be able to find out if they are safe, in my state they would not court order him to release her information, they would only order her to stay away from the children if you found out she was not safe by finding out her name and date of birth, kinda a catch 22.
Since you know a private investigator let them get the information, they have ways to find this out by following her or befriending her or something. Once you have the name and date of birth from the PI, then find out if she is safe or not. If she is not safe go to court and have her removed form the childrens lives, if they marry however you will most likely will have no grounds to stand on. It is then his choice and you will not be able to keep him from his children and the court can not order him to leave his spouse for your childrens sake.
I withheld his last visitation from him, with the intent of filing for emergency hearing...then I didn't know if I should file in CT where he lives and the divorce was finalized, or in NH where the kids and I live now; then I lost my job (have another one now, but still unnerving)...We have a hearing next week. I have filed a continuance because I need time to file on him for contempt of unpaid child support, and for child support modification. He's also trying to take custody of our oldest, 11yr old daughter. If his live-in girlfriend had custody of her kids all along, and didn't disappear for over a year, this really wouldn't be an issue, but those are HUGE red flags for me. Even right now, I don't care who he sees, I don't care if he hires an independent party to tell me his home and girlfriend are safe. For all I know she had the custody taken away from her by the state, and that her year in "college on the cape" was spent in jail or rehab. Her kids don't even live with their fathers. I'm just hoping the hearing officer will understand my point of view. :(
You have a right to know where your children are and that they are safe. Thats an issue I would take to my lawyer and court. Knowing his address and where to find my children in an emergency is not something I would compromise on at all.