Dubai is very westernized. Your woman should be fine. I lived there for a short time but it was more than 10 years ago. It's hard to drink, it's hard to find pork products; but you can get to them in the touristy areas.
As for what to do, definitely check out the gold souk. It's a large area of shops that sell gold which is cheaper than you can find almost anywhere. The reflection of the gold from the shop windows makes it appear as if everything is made of gold. I bought a watch while I was there, I picked it up for $260 and found out it was a $900+ watch when I got back.
They also have excursions into the desert with a 4WD vehicle, it takes a few hours, and you end up at a fenced in area where they have a huge feast and music with belly dancers. I can't say enough good things about it. I wish I had more info for you, but you should DEFINITELY do it if it's still a thing there.
You may experience some racism, but for the most part the people you encounter will not be Arabs. If you DO run across an Arab who is being rude, or perhaps ignoring the fact that you're in line somewhere, be careful because he is above the law. Even if you're in the right, you could end up in a foreign jail for starting something.
The city is beautiful. Outside the city, there is NOTHING. Take pictures, show them to us when you get back.