Hi! I am glad things are working out with your son, it seems like he has made great progress. Continue to stress to him that completing the program is the single most important thing he can do in regards to custody and visitation with his child. That and remaining on the straight and narrow. Tell him never to give the nutters a reason to deny him access to his child. Because they will.
Considering that she seems to be "popular" I would suggest a DNA test. It would be horrible to bond with, love, and support this baby and find out in a few years that she isn't really his. In addition, in many states once the father signs the birth certificate/affidavit of paternity he is still responsible for child support, even if he finds out later that the child isn't actually his.
Custody has to be set through the court or a mediator. Until your son is given legal custody of that child she is free to remove that child from the state if she pleases. Custody has nothing to do with paternity. Push to get legal custody ASAP.
I have zero advice for this meeting other than be ready to walk out if things get out of hand and be willing to contact children's services if you really think that the child is in danger. Oh, and if you haven't already consult an attorney that specializes in family law.
I am glad that things are looking up for your son. That, in and of it's own, must be a great burden lifted from your shoulders, crazy train wreck aside.
Good luck.