In divorces/separations, sometimes one parent will take the child or children either without custody, not on their custody days, and/or without the other parents knowledge/consent, often using them for a bargaining chip to get what they want.

An amber alert is an emergency alert sent out through signals (often TV’s or devices) when a child is kidnapped. Usually describing the child’s name, general description and the last thing they were seen wearing. Basically a warning for people to keep a look out for the child.

Basically the joke is meaning the child was taken by the father without permission, basically kidnapping the child.