As a rule, it's best not to plug your Airstream's shore power into a GFCI outlet in your garage. When one GFCI circuit is plugged into another GFCI circuit, the "upstream" GFCI sometimes mistakes the downstream GFCI as a fault.
If all of your garage outlets are GFCI, you might want to shut off the GFCI breaker in the Airstream for the duration, just to be sure; the garage GFCI will provide all the protection you need.
"In a perfect world, I'd be given enough time to wrap up one emergency before the next one starts." —Freefall©2013