I have a similar setup. I have an auxiliary battery that supplies power to my carPC when it is in standby. Your load will draw power from whichever source has the highest voltage or if both if one source cannot supply the necessary current. In your pic you have your Ignition running your CarPC, not sure if you mean this is coming straight from the battery or if you literally mean the ignition 12v+ source. This typically is low power and cannot power your PC.
Hope this helps! Check out my build to see my setup.