Quote:...But, when I add it as a layer on top of image 2, image 1's colors change.
Difficult to say without the images you are using, but often
If the base image is in Indexed mode - look at the top of the Gimp window it shows the mode, then anything added will use the limited colours from that image.
Check each image, use Image -> Mode -> RGB to set the colour mode for the first image and try again.