Welcome to the forun Sam.
With the last sentence it sound like you power the camera in a creative manner and that do not work, but it do work when you use the supplied means of power.
The hard wire kit is that a generic one or one made for your brand / model ?
If a system do not get enough power erratic behavior are not uncommon.
It is also not uncommon for rear cameras to not be plugged in correct or the plug in the socket have some strain on it via the wire, people braking the rear camera wire also happen, though i dont quite understand how they manage that as the ones i have worked with have been pretty beefy, and it have never happened to me personal.