The very best thing you could do would be to get an Opus, if you were using a standard ATX PC.
The Opus is a pure DC-DC solution, with ignition sensing and shutdown controller. Do a for Opus and you'll find lots of solutions!
However, as you're going to be using a laptop, then unless you can get a cigarette lighter adapter for it to run it on 12v, then you will have to go for the invertor route. However, that adds unnecessary conversions from 12vDC to 110/220vAC to 12vDC.
If you have an Opus or similar, then you shouldn't need another battery, however some people also have lots of amps at stuff that they want to power seperately to the main car's battery.