How big is this RV?
I think a 13,500 Btu A/C is going to cool the small space so quickly, and will not take the time to dehumidify the air in the RV. A larger air conditioner will cool it even faster, leaving most of the humidity in the air.
I have a 30' long RV that is well insulated (as RV's go) with lots of windows, and 240 square feet of roof. I lived in Phoenix with one A/C unit when some days reached 105 and others 110. While not "Cool" inside, it was cooling the RV and reasonable inside.
So make sure that your roof is white, and get the 13,500 Btu air conditioner. If you plan a lot of winter camping, or using the RV as a extra bedroom while at home, you might consider a heat pump so you can warm the RV too.
Fred.