Wrong... You obviously do not understand GFCI receptacles. They are NOT load sensitive, they detect leakeage between return and ground.
It is obvious to me that the ice maker has a short (or partial short) from neutral to ground, probably at the heater element that loosens the cubes. This condition often occurs in water heater elements.
Why did no one here even bother to ask the OP what kind of motorhome he has? With that information, we could determine if it was equipped to charge the chassis batteries, and thus just failing, or if it was not so equipped.
I used RMP-3 on my 16 year old Bounder about 10 months ago and it still looks great. I bought 10 gallons of it (2 5-gal jugs) during Lowe's close out for $4.99 each. I won't live long enough to use it all.