i would just have a lipocharger in the car(could be turned on/ by relay from arduino so its not running all the time) so when you put your stuff in the car it runs by the 12V through the charger, and when u remove it your lipo starts to lose charge and everthing runs on that.
now this is probably not the best way as it can lower life of ur batt
oh wait ur not removeing it ur turning the car off.
have a acc line from the car run to the arduino split it to a signal, and a line.
(one goes through resistors etc to your input pin the other to a relay. on NO)
use a lm317 voltage reg or something else to reg pwr if u want (or caps and resistors) etc.
your lipo is also connected to the relay. on a NC
carRunning = digitalRead(inputPin);
if( carRunning == HIGH){
dighitalWrite(relayPin, LOW); //relays i like activate on a low others may be high.
}else{
digitalWrite(relayPin, HIGH); // when the acc is off it switches to battery
}
the problem i see is that their will be a short iturupt in power between the 2 power sources.
so add a 9v battery in parral with the relay so it provides power durring the inturupt.
hope it helps let me know if it dont or u need clarification