You run one continous length of #6 copper from the ground bar in the panel and catch both ground rods. The wire will pass through the acorn clamp on the first rod without being broken.
As for the water pipe, you may be confused. If the water pipe entering your home is metal of any sort, you have to run a #4 copper ground wire to it. The grounding connection must be made within the first five feet of the pipe where it enters the house. Your post sounded like you thought you only had to ground the water pipe if it was within five feet of the service entrance. This is not the case at all. If the pipe enters as metallic, you have to catch it with a ground wire within the first five feet.