I fear that "Sharia Law" is amorphous because it derives from "Islam," which itself is not a country or jurisdiction, but a belief system or religious practice.
How was "Sharia Law" formed? Was it through a jurisdiction's legislative process? Was it through a jurisdiction's legal process of interpretation and precedence? What recognized body defines the proper interpretation of Sharia Law for others to reference?
What is the jurisdiction that is the basis for "Sharia Law?"
-PJ
Keep in mind, I posted a link to Wiki, because it's convenient. But, it's convenience doesn't necessarily mean it tells the complete picture. To paint a complete picture with respect to "choice of law", I'd need to provide several links to sites that are shielded behind a pay-wall.
There are dozens and dozens of precedents established for "choice of law" provisions to be based on religious canon law - Jewish law, Catholic law and even sharia law. It (jurisdiction) doesn't necessarily need to be limited to a physical jurisdiction, despite how it's described in Wiki. It can reference a body of law, like a religious canon.
In the interest of brevity (and accuracy) I would point you to several discussions at Volokh Conspiracy. Those links may be found below, and they include discussions about when such application is appropriate (like in a binding arbitration agreement), and when it wouldn't be, like the child-custody case that's discussed. The learned professor, Eugene Volokh, does a much better job of explaining why this sharia business is overblown and irrational.
Why American Courts Should Sometimes Consider Islamic Court Rulings (and Islamic Law)
American Court Refuses to Honor Lebanese Islamic Court Child Custody Order
Court Rejects Claim that AIG’s Use of Sharia-Compliant Financing Violates the Establishment Clause