Ofcourse we are assuming that all women rightfully deserve custody. I have little sympathy for some American women and how they conduct themselves. So if it was between a hard working decent muslim man and some slutty American woman, the custody should ideally go to the father, whatever the adjudicating forum.
And there is always going to some bias in favor of the local resident. Infact that is why we have diversity jurisdiction in Federal Courts - to avoid state courts favoring their own residents. Thus, an Iranian court will likely favor the Iranian father or mother whereas an American court may be biased to towards the American (especially white) parent. In my interaction with most American people, I have noticed that while they respect other cultures, they firmly believe that the American way of life is superior to all. And this plays a huge role in adjudicating matters involving inter-cultural issues. So I would not be surprised that an American court would favor the American parent. For instance, most Americans are terrified at the thought of children growing up having to wear a hijab. Now looking at it from an Islamic point of view, there is nothing wrong with it. Many Muslims women I have talked to actually *like* wearing hijab and do it by choice. But modern American women believe that it is mediavel and for them showing cleavage is the way to go.
So yeah, be careful in deciding who to marry. Many Arab men tend to pretty suave. They have that whole tall-dark-handsome thing going for them. You'll see them in clubs, their beards trimmed or non-existent, drinking alcohol, chatting merrily with women. But that is usually not the real picture. They tend to change after marriage. Most will just become more religious and focus on the family and work. Not that I blame them. American culture has nothing to offer but getting drunk. But some become radical - going to training camps in Afgahnistan etc. So be careful before you marry a Muslim.