I'm with smarty. The 30A extension cord between the generator and the shore line could be adding to your issue. Try the AC at home with and without the extension cord to see if it makes a difference. BTW, stretch out the extension cord as you had while camping. I also have one of these plugged into a convenient outlet in the RV to be able to see what is available from the shore line.
https://www.amazon.com/Prime-Products-12-4058-Power-Monitor/dp/B000BRFTH6/ref=sr_1_2?keywords=rv+120v+electric+meter&qid=1564586020&s=gateway&sr=8-2
I run a 50 ft 30A rated extension cord when plugged in at home. When the house outlet provides 120V, I see 110V within the RV when it is cool out. I see 108V when its hot out. The AC pulls the voltage down to 105V when running.
