Under some circumstances, it is possible to apply foreign law in Japan.  Here are some references.  But be forewarned that even the US embassy has told people who called them that in the case of someone with dual US/Japan citizenship, Japan would probably still consider that person a Japanese citizen and do whatever they could to work things in that person's favor.  One member reported::

The US Embassy verified this when I called them, but  they told me that under this law, the Japanese court is only obliged to try to apply the foreign law. They told me about a recent example of a California couple who were divorcing in Japan, and the court used California law as guidance, but they botched up and misinterpreted that law completely, so one of the parties is appealing, but that doesn't matter. It is of no consequence that they completely misinterpreted California law and misapplied it, the only thing they were obliged to do was to use it as a guideline, and therefore they met their commitment under the law.

A left-behind parent with a similar experience says this:

My spouse naturalized as an American. So none of us, including our son, had Japanese citizenship, the court had a problem since there was NO WAY it could apply Japanese law.  Japanese choice of law principles require the court to apply the law of "common nationality" in such cases. Unfortunately, there was no state that any of us had the same contacts too (My son never having lived in any of them), so they eventually chose California law as my son's state of habitual residence, because, well my spouse wanted to go there. Even though he had never lived there.

But they had to apply California law, you see, which is very good for custody proceedings.

First, there are repeated statements in the law that it is the public policy of the state that parents have frequent and continuing contact with both parents.

Second, it states specifically that the gender of a parent will not be taken into consideration in awarding custody.

Third, it states that the preference is for joint custody, and that if one party requests joint custody, the court can only award sole custody if it gives specific reasons, beyond "best interests of the child".

Fourth, there is a "good parent rule", which states that the court will consider which parent is more likely to grant the other child access in awarding custody.

Fifth, there is a rule that says that absence from the home will not be taken into account in awarding custody if it is due to abuse, or the absent parent indicates an intent to continue a relationship with child.

Sixth, there is a clear rule that says if the court DOES award sole custody to one parent, it will award liberal visitation to the other parent at the same time, or liberal visitation is implied if it does not (thought the statue is clear that the court "shall" do this).

Would you believe that the Japanese court happily ignored all of this clear statutory law to arrive at its conclusion?

If your friend has any hopes that his wife being treated as an American will make any difference...well, unless the court wants to punish her for daring to not be Japanese any more...

It is very difficult to remove a case from a Japanese court into a US court. It is called "forum shopping" and most courts won't touch a case that is already being adjudicated in another place. I thought I could do it because I had the ability to force my spouse out of Japan, but it didn't stop the Japanese court from continuing to adjudicate the case, rendering verdicts, etc. even tho the spouse had left Japan with the child.

About getting Japanese citizenship back, another member whose ex-wife used to be a Japanese citizen but naturalized as an American says:

My ex did try and regain her Japanese citizenship but was denied being told she now had to go through the same process as any other "non-Japanese" must to gain citizenship--this would mean living in the  country for 5+ years, having a proficiency in the language (not a problem), not being a criminal in her citizenship country (should be a problem) and a few other items. She was an adult when she made this  decision so she is looked upon in some bad light I imagine.

She had to officially renounce her Japanese citizenship and provide a copy of her KOKUSEKI RIDATSU TODOKE to complete the US Naturalization process. I have copies of her Naturalization Certificate and her Oath of Allegiance, which may be viewed now, as her thumbing her nose at the country whose laws she swore to uphold and indicate she is a US citizen.  (Yet even then Japan  refuses to help the US law enforcement authorities.)
 
About living there (Japan) she lived there until early 20's and then again for a few years when we were married. She is now in her forties, so she has spent about half her life in the USA.

Note that this "ex" is also being indicted in the US for kidnapping.  She will be arrested if she steps into the US.  So that may be one way to stop her from regaining Japanese citizenship permanently.

Laws In General

See Article 14 of Law 10: ACT ON THE APPLICATION OF LAWS

Divorce Laws

Source:  http://www.pref.osaka.jp/kokusai/OIS_web/english/marriage/04_1.html

Question: I am a foreigner who has lived in Japan for a long time. I am going to divorce my Japanese spouse? What formalities will be needed?  

Answer: According to Article 14 of the Law concerning the Application of Laws in General, the governing law of divorce will be the law of the country of the husband and wife when they have the same nationality, the law of the domicile when they don't have the common nationality but, or in the absence of such laws the law of the place on which they have the most material bearing. Your case will be governed by the Japanese law since both of you live in Japan. Under the Japanese law, divorce by agreement is recognized. The husband and wife may negotiate about divorce and seek legal arbitration at the family court if mutual agreement is not reached. If the matter is not settled by arbitration, then the divorce will be brought before the district court. The causes for which the court grants divorce will be those provided in the Japanese law. If there is a mutual agreement on divorce, you can get divorced by registering divorce. The municipal office of the municipality where the Japanese partner's residency or domicile of origin is registered will accept the divorce registration.

Question: We are foreign couple of the same nationality living in Japan for a long period of time. We want to get divorced. Can we get divorced in Japan?

Answer: Most probably, yes. Since you are of the same nationality, the governing law of the divorce will be your country's law. Unless divorce by mutual agreement is recognized under your country's law, you will be able to get divorced only in a court of law. The Japanese court has jurisdiction over your divorce since both of you have domicile in Japan. First you have to seek arbitration by the family court. If the matter is not settled by arbitration, then you will be able to file a suit for divorce with a district court. The divorce granted by the court will be most probably recognized in your country. However, you had better ascertain this from the embassy or consulate of your country in Japan.

Question: We are a foreign couple of different nationalities living in Japan. Can we get divorced in Japan?

Answer: Yes. But each of you will have to conduct necessary formalities according to the laws of your countries. Since you do not have a common nationality, the governing law of your divorce will be the law of your common domicile or of the country on which you have the most material bearing. Since the domicile of both of you is in Japan, the Japanese law is applied to your case. The causes for divorce are determined according to the Civil Code of Japan, and you can register divorce by conducting formalities provided in the Japanese law. However, the validity of your divorce in your respective countries may be predicated on the laws of your countries.