Well 1, like you said get an inverter, but also like you said, not the best power effeciencey.
You could mount inside a second psu, for the car and add a second plug on the back. That way you use the standard psu at home and the second +12v one in the car.
Personally, i would look for an old PIII or something for the car, brining the unit to and from the house would probably be a hassle. OR check out the classifieds and see if you can pick up something inexpensive for the car.