You most likely have a bad heating element in the fridge. Absorption-type RV refrigerators use heat to cool (I know, it seems counterintuitive) with the heat coming from either an electric heating element or a propane burner. If the heating element is leaking current to its grounded sheath (not uncommon), it will trip a GFCI-protected circuit. A replacement heating element will most likely take care of your problem.
Edit: Sorry, I misread your post. If your fridge ran OK on electric without the coffee pot, it's probably OK. If the fridge will run independently and the coffee pot will run independently without tripping the GFCI but the breaker trips when you run them together, I suspect you're tripping the breaker due to overload, not the GFCI due to a ground fault.
Rusty
2014.5 DRV Mobile Suites 38RSSA #6972
2016 Ram 3500 Dually Longhorn Crew Cab Long Bed, 4x4, 385/900 Cummins, Aisin AS69RC, 4.10, 39K+ GCWR, 30K+ trailer tow rating, 14K GVWR
B&W RVK3600