What is the idea behind the 'Hague Convention' in international child custody disputes?

That issues of custody should be decided in the country where the children normally live (or are 'habitually resident' in Hague language) by the appropriate court. Parents cannot take the law into their own hands , move children around unlawfully and cause them trauma.

States that are bound by the 1980 Hague Convention on the Civil Aspects of Child Abduction are supposed to engage in " first-aid" legal proceedings to secure a fast return of wrongly removed or retained minors, to their 'country of habitual residence'). Defences are limited, and a high standard of proof is expected.