Sounds like you have an open neutral, meaning loss of connection of neutral from your trailer to your source. If neutral is not connected, then it is also not connected to ground. And metering would show 120 vac neu to gnd. That can also possibly damage some of your 120 vac devices depending on how badly the voltage varies on the two different legs.
Since plugging/unplugging temporarily corrects the problem, I would guess there is a loose neutral wire connection either in your power cord connector or in the outlet you are connecting to .
One of these is handy to have for troubleshooting purposes.
https://www.homedepot.com/p/Receptac...E&gclsrc=aw.ds