Umbilical = cord between trailer and tow vehicle
Shore power = cord between trailer and power pedestal at campground or outlet on the side of your house or whatever
You will want to disconnect the negative connectors on the batteries, not the positive.
The wiring varies however on many trailers (including mine) shutting off the "kill switch" does not disconnect power to the 7-way connector. The "kill switch" is useful for being sure that no 12v
power is being used in the trailer during storage, and is useful for maintenance on most of the 12v
system, but it does not disconnect the batteries from the converter or the 7-way.