It's not that the father was granted custody. The mother kidnapped the kids. Even if she were a saint, she doesn't have the right to take them from the father.
It's curious how people tend to defend their countrymen despite mountains of evidence to the contrary. It's easy to paint yourself the victim under a foreign government/individual oppressor.
If this case had happened reverse, where an Argentine dad is trying to recoup his kids from an ex that fled to the States, the Argentine media would be talking about what an evil mother she is and how the Argentine father should be able to bring them back here.
This whole situation is made much worse by the courts being so incredibly slow in these cases. When a child is kidnapped, be it by one of the parents, the law should act quickly... not take years. Five years in the life of a child is a lifetime. They no longer have any connection to the other parent, to the country, to the language, and their lives are basically ripped in two. One could make the case that the kids are better off in the situation they're used to, but that only encourages other parents to break the law and flee with their kids, hide for a couple of years and be home free. That's not right either.
Hopefully the girls adjust well to their new life in the US... and hopefully the mother matures a bit, moves to the US to be close with them, and tries to make the whole process a lot less traumatic for them.
According to everything I've read the father was granted custody, the judge said he was to be the primary residential custodian, and then the judge gave the mother the right to take the kids to Argentina for a two week trip, the father believed she was coming back, the woman stayed. that is how she was able to leave with them in the first place, because she had been given permission for a two week trip. The thing is that during the custody hearings the judge had already indicated that he considered her to be a flight risk, and the father argued the two week permission but it was granted nonetheless.