If you or your wife become UAE residents then you both are entitled to work here in the UAE. Your Sponsorship will come form the company that employs you and your wife's sponsorship will come from you or directly from the company that employs her.
There are always opportunities for various forms of employment here but one needs to look around a bit. There are many new schools or university positions opening up so maybe you could inquire there. The hardest decision to make is deciding to move, or to stay exactly where you are. Once you have made the decision to move, the rest will follow quite naturally.
Dubai is a great place to live and work, but realize of course if you haven't been to the mid-east that it is 'the middle-east' and not downtown London, or Sydney or the US or Europe. So you must remind yourself not to compare apples and dates. The secret to being happy here: You need to make it your home away from home - spend money, enjoy yourself while saving a bit too. One needs a balanced life and so as long as you balance this well, you will find that it is actually a place with a lot of positives and potential.
Good Luck.
