This question is different than all the other "What generator" questions. This generator needs to be BIG to run an old inefficient A/C, possibly 18A, and a new inefficient 14A refrigerator. I'd suggest a Honda EU7000is or a pair of EU3000IS with a parallel kit. The highly recommended EU2200 is not going to run both the A/C and refrigerator together. It may run the A/C or the refrigerator. A big generator is needed to not overload while starting one of these energy hogs while the other is running.
2018 GT27Q, 45 nights 9,860 miles, 600W Solar - Produced 75kWh, PD4655L, 6V Batteries, Champion DualFuel, ProPride&BOSP, 16" tires, 2019 F250 PSD
Sold: 2017 FC25FB, 316 nights 40,150 miles, 400W Solar - Produced 200kWh in 216 days
2013 Casita SD17 89 nights 16,200 miles