Firstly, the weekend here is different - its Friday/Saturday, but alot of people work Saturday.
So the traffic on Friday is light and is the day I'd recommend you drive around Dubai. Saturday traffic is lighter than during the week but not as light as Friday.
If your going to the East coast the traffic there will be fine.
I would recommend doing Palm etc and anything in Dubai on Friday and go to East coast on Saturday.
Driving here is better than the myths - it's like driving in any big city like Amsterdam - you just need your wits about you - and if a big 4X4 comes up behind you at 200kph move out of the way quick - cos they wont wait and they'll get past you one way or another.
One thing to bear in mind is that you can't drive just on an EEC drivers licence here - you need an International Driving Permit in addition.