That's not the case; non-citizens under U.S. jurisdiction also have due-process rights. For example, despite him being a French citizen, Dominique Strauss-Kahn is entitled to the standard Constitutional rights in his criminal trial, including things like being read Miranda rights, not being forced to testify against himself, and receiving a trial that accords with due process. If any of that were violated, he could appeal his case and the appeal would be heard in the same manner as if he were a U.S. citizen being tried in the same New York courts. Even foreign corporations have due-process rights; for example, Texas cannot simply seize a refinery owned by BP without some kind of legal process.
The only cases I'm aware of where it's more murky are: 1) non-citizens held by the U.S. armed forces outside the territory of the U.S., alleged to be "enemy combatants"; and 2) illegal aliens awaiting deportation, who do still have some limited right to due process in challenging their deportation proceedings, but there's more controversy around it.
You're absolutely correct here. The 4th Amendment (giving protection from unreasonable search and seizure) starts off, "the right of the people...", not "the right of the citizens". Together with the 14th Amendment's Equal Protection clause, non-citizens get the same protections.
That said, the doctrine used in asset seizure cases (generally connected to the failed war on drugs) is that it's the seized property itself that is suspected to be guilty, and property doesn't have any of these rights. One can easily imagine them trying the same crap here.
Yeah, on the latter point, I agree that the odds are stacked against any claim. But they'd be stacked against a claim by a U.S. citizen, too; apart from the added expense of litigation, I don't think a foreign company would be at an extra disadvantage in trying to get their domain name back, just the "normal" disadvantage that comes with trying to fight administrative property seizures.
Note: I am not concerned with immigration, but de-facto denial of basic rights and discrimination on the basis of nationality in cases where those rights are basic human rights, and not privileges granted by the state.
This particular linked case appears inextricably tied up with immigration, though. The person in question isn't alleging that he's being denied rights in any manner other than via the fact that he isn't allowed to legally live in the US. That's a bit different from the question of whether non-citizens caught up in the U.S. legal system (in either a criminal or civil case) have the same rights during the proceedings as citizens do.
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.
The only cases I'm aware of where it's more murky are: 1) non-citizens held by the U.S. armed forces outside the territory of the U.S., alleged to be "enemy combatants"; and 2) illegal aliens awaiting deportation, who do still have some limited right to due process in challenging their deportation proceedings, but there's more controversy around it.