It is highly unlikely that any family court would award residence to someone who does not live in the same country, or someone who was not married to the mother.
... or, in this case, someone who has never been within thousands of miles of said child. As far as I understood from the OP, they have never been on the same side of the Atlantic together. Mom left when she was pregnant.
Also, I'm getting a stronger vibe of spite here than of "love".