There is one more critical issue that you need to decide early one. Do you want this thing to be waterproof as in "dunk it into water is OK" or do you want it to be water tolerant where it does not mind getting wet, but will get into trouble if it is submerged? Water tolerant is a lot easier than waterproof.
I am not familiar with waterproof speakers. A quick google search suggests that they are the "don't mind getting wet" type and not really waterproof. You will have to cut a hole in the box and mount them with appropriate gaskets etc to make sure the box is not flooded.
You can buy any old portable ipod amplified speaker and take out the amplifier from it. Or you can do a google search for "audio amplifier" and get dozens of hits. You will need to do the wiring for the battery and the ipod connector. You may need a power supply board to get the 12V battery to a lower voltage. You can buy or build that depending upon your level of knowledge and ability. But I suspect you should not have a problem getting an amplifier that runs directly off a car battery.
Getting a pot to be waterproof or even water tolerant is not an easy task. There are audio pots available that have environmental seals in them. They are not cheap or easily available. You can mount one of those through the box. You would be better off finding an audio amplifier that has "volume up" and "volume down" buttons rather than a pot. That makes life a lot easier because it is much simpler to have a waterproof push button switch.
You need to be really careful about mounting and securing the battery. If there is a shock, you do not want the battery to come loose and touch something that shorts its terminals. That could result in a fire or maybe even an explosion, which is never good.
I am sure others will have other ideas or more specific recommendations.
---55p