[steand]

jyl's Idea with a relay is OK, so you only charge when ignition is on.
A simpler solution is to put a diode in the wire that feeds from the +12V in the car harness to the battery, and tap the video power directly from the little battery. The diode will See to that the +12V from the car will not be able to draw any current back from the little battery (only if you have a higher voltage on the little battery, as in if you remove the big battery). The diode will looSee some 0.7V across it when charging; but that shouldn't be a problem, since the car generator normally brings the voltage up to +14V. The diode should be a rather big current rating one, like one used in big power supply's.