Do you mean that your power converter uses an ungrounded adaptor? If you can carefully inspect your converter see if it has the words "Made in China" on it, if so mark all the wires , remove it and use a 20 lb. hammer to reduce it to something that can never be hooked up to electricity again. Next go out and buy a comparable size USA made converter by http://www.progressivedyn.com/rv_converter
or a couple other makers and install it in its place, this should cure the problem and prevent burned up batteries and smoking converters. When you isolate the ground you defeat the GFCI. My other question is why the converter would be on a GFCI in the first place, most are direct wired to an individual breaker, The 12volt DC cannot utilize ground fault circuits, they are AC only. The only RV receptacles that must be on a GFCI are the bathroom, kitchen and outside ones. Most RV makers daisy chain these to one GFCI receptacle in bathroom. Also if the GFCI has been subjected to a nearby lightning strike or severe voltage surges it is probably bad and needs to be replaced. Also the 2009 Electrical code lowered the trip point on GFCIs from 6Ma. to 4Ma. so newer ones trip in uses that older ones did not.