I ordered a new fifth wheel with the Norcold 12 cu. ft. piece of junk. Within 6 months I ripped it out and installed a Samsung residential. It will be 6 years ago in August and have never looked back.
At the same time, I swapped out the single battery to 2 6 volt golf cart batteries and inverter. I also added a 160 watt solar panel because at the time the RV was stored at a storage lot. I also wanted to peace of mind of having enough power.
We have never had an issue with power. The inverter is dedicated to the fridge and the solar to the batteries. I suggest getting an inverter no larger than needed 800-1000 watt max and get a decent quality one and be sure to mount it in a well ventilated area. Also, be sure the refrigerator is energy-star rated to keep power consumption to a minimum. At the time we did our swap-out, the Samsung was the most energy efficient of units out there.
You will LOVE it. We have never once regretted it. Good luck.