Two GFCI's on the same circuit in my RV. One works. One doesn't
I've recently started working on a similar issue with an inverter from one of our work trucks. The built in GFCI failed, so I replaced it, but no luck.
It turns out that Modified sine wave devices often cause problems for GFCIs because, apparently, of the harmonics that exist when it is not a proper sine wave.
I found, after much deep googling, a couple older articles from Xantrex, the manufacterer of my particular inverter.
This article is from 1997. It states that you should not test a GFCI when it is active and not under load as it will definitely trigger the GFCI. However, all GFCIs since 2015 are required to be selftest.
This article is from 2005 and talks about how even with non-self-testing GFCIs, some will work with some inverters and not others because of the peculiarities of the individual circuits. It contains a chart where they have done some testing with their array of products against a variety of GFCIs. Unfortunately, that was 13 years ago and of course, none of those part numbers are available any longer. Again, all manufacterers were required to make all GFCIs self testing by UL 943 effective June 29th, 2015.
I have been attempting to make contact with an RV technician to find out the scoop on what they are doing currently, but so far have had no luck.
For your situation, I feel that this explains why the one GFCI works when you feed line power or when you installed it in the house. I'm not sure why you're not having a problem with the other one. Are they the same model? Perhaps it's just luck of the draw manufacturing variances.