I'm proficient with HTML, but have a client using CC to do their own updates to their website. Becuase I have specific code in regards to images (placement, floating, etc.), I am trying to find a way for the client to use CC to replace an existing image with the visual editor. We've tried using the browse button next to the Src window. This works, but it also puts the file path in the HTML! So it works on her computer, but does not work for anyone else.

Besides directly editing the HTML, is there a way to replace an image and simply have the file name show up in the HTML? I tried deleting the file path in the Src window, but it chenges back when I move the mouse.

try changing the name of the images? That's always the easiest way. Just rename the current image, then change the new image to the name in the HTML path already.