Abduction
Abducting a child is a serious business. It's a criminal offence (punishable by imprisonment) whether the abduction is to another country or within the UK, to remove a child from the parent with whom they have been living. It includes a refusal to return a child after a contact visit.
So, if a child is removed in circumstances amounting to abduction, all sorts of emergency procedures can be brought into action. All Courts have emergency contacts, and a judge can authorise various orders, such as 'port stops' and 'seek and find orders' authorising court officials and the Police to locate and protect a child.
It may be a storm in a teacup. Children spending summer holidays with the other parent may not want to go home at the end of the holiday. The rule is that, unless there is strong evidence that they will come to real harm, they must go home while an application for change in residence is pending.
Or it may be a case of abduction to a foreign country. The UK is party to the Hague Convention, which requires the immediate return of children to their home jurisdiction unless certain exceptions apply, which covers Europe, America and Australia - but not Africa or Asia. Governments in Convention countries have special Legal Aid procedures to help parents whose children have been abducted.