If you are European, British or most commonwealth then you can drive on any licence in the UAE. Until you become resident. As soon as you are a resident you need a UAE licence not to drive but only to insure a car. So if you rent a car you can still drive on your licence if you are from the above countries (as does everyone on holiday who needs to rent a car)
If you have a family and 2children I would suggest you want a house not an apartment and I had colleagues live in Mirdiff, DSO, The Villa, Falcon City, Victory Heights, Arabian Ranches and Motor City. There are guys in The Lakes, The Springs, The Greens etc but now that FDB is firmly operating from DWC and DXB I would firmly suggest DSO, The Villa or Arabina Ranches. Just for your commute and also for the childrens schools.
Of course it depends on what sort of quality of life you want and what also you expect but your spouse and children spend a lot of time in thier house and getting an apartment just doesnt seem worth bringing them to Dubai IMHO. As always its all about cost if you think 40-50% of your salary on accomodation is normal (as is normal in UK) then you have a lot of choice. If however you are one of these people who believe that the "accomodation allowance" bears any relation to actual accomodation rather than just a way of keeping your pay element small wrt to your final payment when you leave then by all means please come on here in 12 months time and whinge about how you cant find an apartment for 140,000 per annum that suits your needs and locations!
Re driving if you do not drive in Dubai you life becomes very difficult very quickly you and your spouse need to drive. I know families who didnt have both drive. Their life was a nightmare. You dont want to be getting taxis everywhere you just dont trust me! There is no location in Dubai that allows you to walk to decent shopping AND walk kids to school AND has decent transport links unless your idea of a good school differs from KHDAs.