One other issue is state of charge (SOC) and amps. Some people like to count amps in and amps out.
The ambient temperature will impact how often the fridge runs as well. As you noted, when you open the door a lot of cold air spills out and then the fridge has to run to recover. I'd expect to get more than 12 hours out of my fully charged batteries.
There are simple 12v voltmeters available on amazon. Do you have a cigarette lighter style plug connected to the house batteries? There are also simple voltmeters that plug into those. Of course there are many options for doing all this.
Balmar has a couple options for monitoring batteries. Scalf77 has recommended a couple over the past year.
Sounds like your batteries are taking a charge, just not lasting as long as you would like. As you know, they get weaker over time.
I went with a Balmar SmartGauge last year:
Smartgauge Battery Monitor | Balmar
Balmar now has a newer product:
SG200 Battery Monitor | Balmar
Scalf77 should come along at some point and hopefully offer his opinion.