Aussie,
You can do pretty much anything you want to in this country so long as it is in reason. As said before no drinking on the streets or being totally bolloxed in public, you wont be deported unless you start assaulting the police. You will however spend a bit of time inside. Would be worth getting deported before that happens...
Your wife will be fine but suggest she doesn't wear tiny clothing. She wouldn't get touched up or assaulted but would receive many long lingering stares and people assuming she is a Russian hooker.
This has to be one of the safest places for anyone to bring up a child and for your wife to live
Find yourself a book called "The Dubai Explorer". It'll tell you everything you need to know.
Hope it helps and if you can, get oyurself and family to DXB for a long weekend and spend it with people who live here and go out with them doing their everyday bits and pieces rather than taking the tourists out.
