Legal Question in Family Law in Kentucky

Kidnapping, no. Custodial interference, possibly, if there is a custody order in place, but generally custody disputes that violate a court order are handled in family court, not criminal court. Likely though, if they've been living together since the baby was born, he probably isn't ordered to pay child support, and probably there isn't even a determination of paternity (just being on the birth certificate is not enough to give the father of a child born out of wedlock parental rights, a judgment of paternity must be entered), let alone a custody order. That would mean she is the only legal parent, and she can go wherever she pleases... at least until he files for custody.