I don't think it would be considered kidnapping, but the biological father could go to court to get a custody agreement and might be able to get one favorable to him that would prohibit moving the child either explicitly or by requiring a certain visitation schedule that won't work if the child is far away.

It's actually pretty hard to get sole custody without visitation requirements unless the other parent is documented as being dangerous. Even then, the court usually sets conditions under which the other parent can regain visitation rights.

The biological father has money, and that's the key thing for that sort of legal maneuver. So the question of moving away is one that the biological father has to be on board with.