I was thingking about this today. I'd use an Orinoco EC or EC/S (with serial) (Ethernet Converter) you'll need a PCMCI wireless adpter too. THe EC is just a small box for retro-fitting 10baseT equipment to be wireless. Be prepared to spend some $$$

You can then power it off the car battery.

Yeap, you'd need a MOSFET transistor. Works like a regular transistor but work off voltages. Power & heat dissipation should not be a problem.

If you wanted to do it proper, you'd have to come up with a way to turn it on when you turned the car off and then keep it on until the player turns off.

if (~car_on & rio_on) have EC on.

Any EEs out there?
I'll try to remember to ask one at work tomorrow