AC should be able to drop 15 - 20 degrees between intake and outlet air. Start with that measurement and then go looking for the problem later. We had a Dometic 15K OEM in 2013 and a replacement Dometic 15K in 2015 that both failed due to pin hole leaks in the evaporator with loss of Freon. Had exactly the same symptoms as the OP. Replaced with a older Dometic unit made in Elkhart instead of China that is running strong with about a 15+ degree drop. While the quick cool dump will cool quicker after a hot day with no AC, if you have to park in the shade, insulate your windows, etc., then you probably just don't have enough AC capacity. Folks have commented on line that having 2 ACs helps get things cooled down quickly, sometimes allowing one of them to be turned off after that.
