I have a question regarding divorce in Islam while living in the USA. I separated from my wife due to some domestic issues that took place between us 10 months ago. While separated, I decided to divorce my wife due to the gravity of issues. As I did not want to utter the word Talaaq (divorce), I hired an attorney to do the job for me in compliance with US Law; we both waited for the legal period of time for divorce to be granted by the judge. On 7/19/2016, the judge granted us a divorce with the statement of right of information for us that I am copy pasting for you to read:
"Within the thirty days following the date that the divorce is granted (7/19), the court can vacate the divorce and restore judicial proceedings which will have the effect of reinstating the marriage as though it never happened. If reconciliation is going to occur, then both parties would move to dismiss their individual claims (nonsuit their claims) and the divorce proceedings end. Getting that done requires both parties to agree to both parts of that process. If both parties do not agree to ask the court to vacate the divorce, then the judge is unlikely to do so without a clear legal reason why the divorce is defective. That is unlikely when both parties agreed to the divorce decree. If your wife agrees to vacate but does not agree to nonsuit her claims, then she can still move forward with the divorce on her own, even if you do not want it. Or vice versa."
Knowing that Islam also gives 30 days period to reconcile from the date of the first divorce, my wife raised the question whether those US court procedures are in accordance with our Islamic law. Please provide us with an answer under the Islamic law that clears the confusion on whether our marriage is still valid or not given that we have reconciled within the time frame (30 days) granted by Islam as well as by US law. In civil divorce, there is just one final divorce that equals three. Do you think that we can reconcile Islamically, or is the divorce final?

All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger. 

The divorce issued by a civil court run by man-made laws has no legal weight in the eyes of the Sharia, as was stated in a fatwa issued by The Fiqh Council of North America. The resolution of the Fiqh Council of North America reads: 

“If a man divorces his wife in accordance with Islamic Law, then there is no harm in documenting it in a civil court that is based on man-made laws. However, if there is a dispute between the spouses about the divorce, then the Islamic centers play the role of the Muslim judge where there is none, after carrying out all legally required procedures. Resorting to civil law to end the marriage does not on its own dictate the termination of the marriage under Islamic Law...”

If the husband has not issued a divorce by a verbal or written statement with the intention of issuing a divorce, then it does not take effect and the marriage bond is still intact.

The Raj'ah (or Rujoo', i.e. revocation of divorce) prescribed by the Sharia has no relation to the thirty-day interval mentioned in the question. Raj'ah takes place in a revocable divorce that has actually taken effect. If this is not the third occurrence of divorce, then the husband is entitled to revoke the divorce and take his wife back in marriage without the need for a new marriage contract as long as the ‘Iddah (post-divorce waiting period) has not expired yet. Allah, The Exalted, says (what means): {And their husbands have more right to take them back in this (period) if they want reconciliation.} [Quran 2:228]

The ‘Iddah of the woman who menstruates (is of child-bearing age) is three complete menstrual cycles after the divorce. If she does not menstruate, then her ‘Iddah is three months. If she is pregnant, then her ‘Iddah ends when she gives birth to her child. Allah, The Exalted, says (what means): {Divorced women remain in waiting for three periods.} [Quran 2:228] Allah also says (what means): {And those who no longer expect menstruation among your women - if you doubt, then their period is three months, and (also for) those who have not menstruated. And for those who are pregnant, their term is until they give birth...} [Quran 65:4]

For more benefit, please refer to fatwas 82541 and 86952.

Lastly, it should be noted that it is impermissible for the Muslims to refer their disputes to regular courts run by man-made laws except in a case of necessity. The Muslims in non-Muslim countries should refer their disputes to the Islamic institutions and centers responsible for settling the disputes of Muslims.

Allah knows best.