Interesting... The GFI shouldn't effect the Air Conditioner. It's on it's own separate breaker. You may have a wiring issue (is it under warranty?).
We had an issue with the low speed fan, and it turned out that the rotary switch had gone bad. Got a replacement on eBay for less than 20.00, and it was easy to replace.
Me, My wonderful Wife, 2 Bluetick Hounds, a Newfie, a Cairn Terrier & a Black Lab / Newfie Mix.
2018 Jayco Alante 31v