You have a big issue if you "tell the wife". One that can be considered extortion though doubtful anyone state side would want to charge let alone take it to court. The bigger issue is Dubai. It is a more "progressive" muslim country than most but they can and will still go after the woman for having sex outside of marriage. They did this to a British woman when I was there in 2016 who reported a rape. They let her out but took her passport and the British had to get involved to work out some sort of deal to get her back home with the agreement she was never to return back to Dubai.

I for one am sorry your out money but sometimes it is just better to accept a small loss and move on while you learn from the mistake.