Mark,
In my neck of the woods, only one ground rod is required unless the inspector determines that you have more than 25ohms resistance on that rod. Then one more is driven and they are tied together.
On residential, the local power company does not want a ground in the meter, but requires it on commercial installations.
In the installation you have described....... it creates a parallel path to ground which is strictly prohibited in the NEC®. The electrical system can be grounded at any of 3 convenient spots, the service drop, the meter, or the first means of disconnect, at which it must tie to the neutral. Any other connections will create a parallel path.
Now, there are exceptions, as anyone that is familiar with the NEC® knows. If you have metal underground water pipes, then that is your main grounding electrode and your ground rod is supplemental.
After the first means of disconnect, the grounds and neutrals must remain isolated from each other, to maintain a low impedence path back to "ground". That ground is not your ground rod, but the power company's neutral. The ground rod is basically for dissipation of excessive voltage....i.e. lightning. Nothing more.
Now back to the water lines.......they need to be BONDED to the service neutral at the first means of disconnect if there is plastic coming in underground.
Sub panels should never be connected directly to the grounding electrode system, as they are grounded by the cable that feeds them. Of course that changes if we're talking about a second structure fed from the same source......another one of those exceptions.