I just got home and read all replies. I'll attempt to answer all.
Generally I'm deep in the national forest or way out in the desert. My closest neighbors are miles away. I usually only run the big generator for 2 hours mid-morning then 2 hours early evening. I do have micro inverter but it really drains the 2 onboard deep cycle batteries.
The new quieter generator, when running and plugged to trailer reverses furnace circuit and a/c. When the big generator is running everything works normally. I did notice on the little generator it does have grounding post for wire, but nothing in the manual says it MUST be grounded. And if it does need to be grounded, would I go to the trailer chassis?