In response to the OP's question about replacing the GFCI...
I have found that the GFCI outlets are cheaply made and not particularly suited to a moving RV. When mine started acting up, I went to Home Depot and purchased a breaker for the breaker box that matched the amp rating of the original breaker and provides GFCI protection. The breakers are much higher quality and I had no further problems. I replaced the GFCI outlet with a standard outlet.
Here are some photos of a couple of typical GFCI breakers. Some breakers have yellow, white or even green buttons, but all have a button to test the breaker's GFCI feature. The GFCI function trips the breaker exactly as an overload or short would.
You'll have to buy the breaker that matches your exact panel in your RV. Take the old breaker to the store with you and they'll be able to find and sell you one...They cost around $30
Bobby & Darrell Mukaisu
2005 Monaco Windsor 40PST 400HP ISL Cummins
2014 Chevy Equinox LS - Full Timers Since 10/1/2010 and Loving it!