Integrating 12v "ups" to a portable fridge
I see two potential problems with your circuit.
The first problem is battery protection. Li-Ion batterys need a proper charger and protection circuit or they can be a fire hazard. There are Li-Ion cargers that have a wide DC input range an should be used here. The battery pack should also be protected from overdischarge. There are Battery Management Systems (BMS) for that. Both the charger and the BMS can be found cheaply in the RC Hobby sections (e.g. HobbyKing.com).
The second problem arises when the user plugs the AC and the DC in at the same time. Either the powersupply or the DC in has the higher voltage and current flows in reverse. When the user plugs an almost empty car battery in the DC in and also plugs in the AC, the car battery will draw a lot of current, potentially killing the SMPS in the process. The simplest way to fix this is to add some diodes but they need to be very big ones due to the current. A better solution would be a switchover circuit.
Here is the updated diagam:



simulate this circuit &ndash; Schematic created using CircuitLab
not pretty but hopefully the point comes across