your car in Beijing. I think that the same is true for Shanghai. If you do not have a 上海户口,register the car under your friend or family or your companies' name. If you drive anything better than a Jetta, it is pretty safe to say that you can affort an experienced driver. It is 1500 Yuan/month. The driver is so cheap, why not have two: one for the day and one for the night shift, unless of cause, you want to show off your 飘移skills at night.
Yes, special permission is required for the out of town car to drive in Beijing and police do pick on the out of town cars. Get a 军牌. That takes care of everything.