My response:
I'll try to be brief - - but, it will be difficult.
You need to see an attorney to do this.
You need to obtain "legal custody" - - not merely parental authorized "custody." I'll give you one example: If you don't have the legal authority, i.e., legal custody with court orders, you won't be able to register him in school, yourself. You'll need Dad to do all the signing and, the school doesn't have to discuss any matters with you. This "inconvenience" will occur throughout his schooling while he's with you, and in many other situations also.
With "legal custody," i.e., "In Loco Parentes", the school will have to deal with you, just as if you were the minor's parents.
There are other situations where you'll find that you won't be able to do anything unless you have the "legal right" to have custody.
As another example, what if he gets into trouble with the law ? The court will not let him bail out into your custody - - because you don't have a court's authority to have custody of the minor in the first place. It would be like having a minor bail out into MY custody. Courts do not release minors to just anyone, you know.
I'm not saying that anything like this will happen, it's just that it's a possible scenario, and if you don't have custody, the criminal court will make him a Ward of the State, and place him into the Foster system - - and there's not a damn thing you could do about it.
You could wave those papers the father has signed and notarized like a flag, all day long, in front of a school administrator's, or a judge's face. It won't matter.
I think you folks may have waited too long to have this handled in a timely manner - - especially where school registration is concerned. But, like I said, this is not the only situation where you may be too late.
IAAL