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Yes, then under the circumstances I believe that a court would give you primary custody of the child.
Where does the child want to live?
First, because of the age of the child - that although he is not of the age of majority or emancipated - he can inform the court with whom he wants to live if the judge deems him mature enough to make the decision. His being almost 16 would seem self-evident that he's mature enough to know what's in his best interest and where he wants to live.
Second, I would go file an emergency motion for primary custody with the family court to make sure you obtain a court order. I'm sure that, under the circumstances, the court will award you temporary primary custody of the child. Thereafter the judge will list the matter for a full hearing (if necessary).
Prior to that hearing - I'm sure if she's any type of mother and has any sense and realizes with whom the child wants to live with and with the pending charges against her - that she will realize she's fighting an uphill battle and will just consent to your being the primary custodian of the child.
That although you haven't adopted the child - the court makes a determination based upon "the best interests of the child(ren)" regardless of who is involved.