In one case three years ago, a Japanese woman's marriage to a Swedish man collapsed and she brought their child to Japan. Later when she traveled to the United States by herself she was detained, as police in Sweden had put her on an international wanted list through Interpol for child abduction. She was sent to Sweden and put on trial.
The Hague Convention on the Civil Aspects of International Child Abduction bans people from taking their children to their home country after a collapsed marriage without confirming issues such as custody and visitation rights. The convention has about 80 signatory countries, mainly in Europe and North America, but Japan is not one of them.