I don’t know under what circumstances the FBI gets involved in parental abduction/kidnapping but I do know that they sometimes do. A woman that we know had her son abducted by the father and it was the FBI that tracked them down and arrested him. He was charged with a federal crime. That man was not a Muslim extremist though- he was a cowboy.
Kidnapping that happens interstate is one of the things the FBI made its reputation on.
I believe when it crosses state lines, as this one did.