Friend of mine (both non-muslims) went to Dubai court for filing a divorce (wife cheated). They went for counseling section twice for feasibility, required before filing to the court. It means that it's possible to file a divorce here even the marriage was not here and both are non-muslims.
Before going into a battle in court (involving child custody), he's looking for reference (book/softcopy) of divorce law (UAE) and/or laywers (if not too expensive).
Any help?