Your inverter and your UPS are too "small". You have too much electrical load attached for the power ratings of those devices.
Why is there a UPS in there? A UPS (to the first-order) is just a battery + an inverter... which you, obviously, already have in your system.
Also this is NUTS inefficient...
Battery (DC) --> Inverter (AC) --> UPS (DC) --> Devices (AC) --> Device Internals (DC)
You are converting DC and AC at least 3 times. Each time you lose about 20% of the power. So you are wasting half of the battery energy (e.g. it is running half as long as it could).
The reason we have a UPS is in case the battery bank runs dry we have
time to hook a generator.
Monitor the voltage of the batteries and "hook a generator" when the voltage drops below 80% of nominal.
You can use a $20 multimeter for this and just check it every half-hour or so. There are also off-the-shelf devices for this.
That will be much cheaper, simpler, and more efficient. It will also improve battery runtime, produce much cleaner power, and continue to operate during the transition.
The tiny battery in the UPS will likely not be able to provide the instantaneous power to keep things running since it is much smaller than the larger batteries you use for primary power.
Can you explain how we can eliminate the building fault with this
current configuration? Is there a way to create a ground?
uh... ground it! ;-) Connect the center pin of the UPS's power cord to a copper pipe at least a meter long and bury the copper pipe in the ground (vertically if possible -- e.g. so it's at least a meter deep).
This will only work if you also have a ground-post (connection point marked "ground" or with the Earth Ground symbol) on your inverter that you connect to the same pipe.
If your inverter doesn't, I agree with @Johnny when he says:
I don't think there's a safe way to eliminate the warning light while
plugged into a portable inverter, and there's probably not much need
to do so since I haven't run across a UPS that refuses to operate when
that light is on.
You can buy copper electrical conduit pipe from a home improvement store for a few dollars.
I should also point out, that the goal here is simply to get the ground-fault light to turn off (by grounding the network). My suggestion should in no-way be considered a lightning protection system. Nor does it make use of anything that would give you ground-fault protection. Further, it probably doesn't meet the US National Electrical Code (NEC), which calls for a maximum 25 Ohms (DC) to ground. Typically, more than twice my recommended length is used to insure compliance.