OK, I see it is an 8 or 10 cu ft 12V Norcold fridge and you have no inverter, nor any absolute need for one as the fridge runs directly from 12V.
In my experience that fridge will draw 75 or so amp hours daily. That will run your single battery down in a half a day if you mind the 50% discharge limitations.
If you want to dry camp with such a DC fridge, lithium batteries are essential. I would install a minimum of 200 amp hours which will carry you for 2-3 days without sun. Then supplement that capability with 300+ watts of solar panels. Scrap your 10A controller since it is too small for the additional panels and replace it with a Victron, Renogy or Epever MPPT controller of at least 40 amps capacity.
If you want to recharge your batteries using your generator, I would upgrade the charger from what you have which is a cheap WFCO 55A with an 80A Progressive Dynamics 9160ALV lithium specific charger. This will recharge the batteries much faster.
See, complex questions result in expensive answers ;-). And FWIW I think Thor and your dealer should be shot for selling you an RV with a DC fridge with only a single lead acid battery to power it.
David
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