The state should enforce visitation and joint custody rights. Whether it is by giving the foreigner a right to stay in the US, or by enabling and enforcing the travel of the child is up to the US government. I think that will be fair enough for those foreigners who are citizens of another country. It is slightly more complicated for refugees or stateless people, but it still should be on similar lines. Anything less is a travesty of human rights and justice.
Japan gets a lot of flak for their policies on this issue, but it should be dealt with in all countries and for all people, including illegal immigrants, deported people or unpopular groups because while the state or people can choose to deport someone, they shouldn't ever be able to steal your kids. The post I linked to seemed to be using it as an immigration issue. That is not what I am arguing though.
Japan gets a lot of flak for their policies on this issue, but it should be dealt with in all countries and for all people, including illegal immigrants, deported people or unpopular groups because while the state or people can choose to deport someone, they shouldn't ever be able to steal your kids. The post I linked to seemed to be using it as an immigration issue. That is not what I am arguing though.