charger cutover circuit

ok, so i got a 12v 200 watt personal heater this winter, sometimes im in my car and can plug it in to the cigaret port to power it,
when im out of the car i also have some beefy LiPo batteries which get me 20-40 minutes of outdoor heat, they come with lipo charger...
I am hoping for a configuration where it will auto charge batteries and power device when im plugged in to car and switch to lipo power when not plugged.

what is best strategy to do this? ... maybe some sort of sneaky switching circuit>?

thanks!

A simple SPDT relay should work.

Power the coil from the car connection.
Connect the car power to the Normally open contact.
Connect the Li-po to the Normally closed contact.
Connect the heater to the Common contact.

When connected to the car battery, the coil will energize and the car power will be feed to the heater.
When the car power disconnects, the relay opens, closing the contact from Li-po battery.