You usage is not obvious: a few hours, 24/7, etc. The SUV plug can power the refer but not battery charging. You'll need larger SUV wiring and/or a DC-DC converter and both have losses. Plus some newer vehicles don't fully charge the vehicle battery - rather reduced charging to help with the EPA mileage. In addition the alternator and vehicle battery are close which is part of the charging design. A remote battery - thinking in the back - ie the starting battery is charged while the remote battery not so much.
Consider a DC-DC converter that can be set for Li or AGM or whatever battery type and alternator load.
