K.S.
I would stop trying to go through the family. it's obvious that they don't care to get involved or don't support him in getting involved. When you contact them you may come off as desperate or starting drama and they will be turned off by it. Just go straight to him.
Child support enforcement will not give you his information, but they will forward a letter to him. talk to your caseworker and let them know what you intend to do. then send the letter to your caseworker with the letter to your ex in a seperate stamped envelope. She will address it and send it for you. Ask her if she needs the letter to be sealed or if she wants to read it to check for any threatening information. If she won't do it (she probably will because I used this process before) you may have to hire a private investigator to find him.
In the letter be very polite. Don't metion money, or make him feel guilty for not being there. If he feels bad he will go on the defensive. Just tell him that your daughter is going to be 12 and she has asked about him. tell him that she would like to meet him and that you support them having a relationship. Don't give specifics or get into visitation or anything. Stick to the basics. Tell him that you would love to have him over for dinner and if he is in a relationship he is welcome to bring his family along as well. Give him your phone number and leave it at that. If your daughter would like to send him a letter enclose it as well. Encourage her to keep it simple and not ask any questions that may be too hard for him to answer. (such as where have you been, why don't you visit etc.) Let her know that she can save those questions for a later date.