The GEC is based on the largest service entrance conductor (in your case a #2). However, if you run it to the vicinity of the panel, you can tap it based on the main OCPD (which in the case of the 200-amp panel would be #4).
As far as your second panel located remotely, if you are not installing disconnects at the meter socket, there may be some question with regard to grouping of service disconnects. You should seek prior approval for your design.