Not everything works with a MSW inverter. However some GFCI's don't work with MSW inverters. Look up your inverter specs and find out what GFCIs are recommended and change to that type.
Is the MW original? Any changes? Good suggestion to check the inverter settings. Also check on shore power. Charger/inverters often pass AC power through when it's available.
I'd bet a donut that everthing worked perfectly when new and something has changed. But inverters and GFCIs do develop problems.
PSW inverters are better in that the output is very close to the utility sine wave output.
I suspect you have a charger/inverter unit perhaps with a built in ATS and remote. As such you definitely won't find one for $600. $1500 plus installation and you're at $2000+.
