Errr.....
Dubai is in UAE.
In UAE, if you are raped and go to the police, you can be arrested for having illicit sex. This recently happened to a British woman. And she wasn't even accusing a UAE citizen - it had nothing to do with the government trying to protect its own men from a foreigner's accusations (which would still be appalling but somewhat more understandable). She was accusing two British male tourists. She was raped; she asked the police for help achieving justice, and they did exactly what UAE law entitles them to do: they arrested the victim on the grounds of being a slut. They confiscated her passport, held her in a UAE jail, and threatened her with prison. (I believe the British government secured her release about a month later... but can you imagine what that must have been like for her?)
That's the law of the country you propose to go to.
That's the country and culture you're supporting with your tourist dollars.
Additionally, if the kids' dad is a UAE citizen (and/or if he is any kind of Arab or Muslim) and decides to kidnap the kids while you are in UAE, you will have little recourse. The custody laws are entirely on the side of the male.
I happen to know this because my ex is, in fact, from that part of the world and I had to take a lot of careful measures to ensure my children weren't stolen when things went south between us.
I wouldn't go to a place like that. Wouldn't risk my safety or my kids' safety. And wouldn't pour my money into such a place. It's a bit like visiting S. Africa during apartheid, IMO: why reward a monstrous system by throwing your dollars at them? UAE has worked hard to paint a veneer of "Shiny Arab Disney" all over themselves, but it's a bit like a dystopian novel: under the shine, it's a slave society that runs on injustice. You'll see the smiling men in the expensive suits, welcoming you with western-style handshakes and elaborate courtesy. You won't see the Ethiopian maids whose passports are held by their employers and who endure every kind of hell with no escape from their enslavement.
Up to you, though. At the very least, if you go, arm yourself with knowledge of the law.