If she illegally took the baby across state lines, could the FBI be brought into case? Could a federal judge over-rule the local judge?
It's complicated - in most cases the UCCJA is the rule which is a carbon-copy law adopted by all 50 states which recognizes which state has jurisdiction, and requires judges to defer to that state. In this case the jurisdiction is Maine, and Kentucy is required to give "full faith and credit" to the Maine custody determination.
Once custody has been determined, however, and that has been done here, the custodial parent has all primarly rights - thus, anyone else taking the child without the custodial parents permission is kidnapping that child.
When this is done by a non-custodial parent, this is called a "parental kidnapping". The FBI does enforce those cases.
Looking closely at this case, the mother is in custody, and will be returned to Maine, I see. The child, though, is in the hands of the state. The accusation of domestic violence, even if frivolous, has started a chain of events that can quickly spiral out of control. Dad is "guilty until *proven* innocent" now.