Question About the Ground Wire on Aux Attachment Circuit for my Car
This is an issue with what is called a ground loop. When you have a device that powered by its own internal battery ground loops aren't an issue, but is an issue otherwise.

The simplest way I know how to explain a ground loop is that when you have 2 devices that have grounds at slightly different potentials they will start to fight with each other causing an audible hum to enter into your sound system.



This is a simple diagram of how your grounds will be connected. In an ideal world your wires has no inductance, resistance, or capacitance. Also in an ideal world ground is ground is ground. However, we don't live in an ideal world. In our world our wires have a resistance and you can generate a slight voltage difference between the ground of each device. When each of these devices creates its slight voltage offset on its ground lines, I am sure you could start to imagine a nasty problem to solve in order to determine whats actually going to happen in the loop. In general a resonance will be found in the fluctuations of voltages on the ground resulting in the hum I mentioned before. In addition to this, a loop like this can pick up lots of noise from the environment around it.

Now, if you leave the connection between the car battery and interface disconnected you leave a single ground path for current to follow. As you add more devices you will want to follow a star or tree style topology. These topologies will remove all loops preventing all of the issues I described above. You will still have cases were there will be slightly different ground potentials, but this isn't a huge issue as they won't be having to battle with each other.