michelle mears from south florida bred up those registered dogs with the red noses....i don't know enough about what made up her lines too tell you if your dog's are out of her stuff, or how they are related, but that's where it comes from......
too further the point, i don't know if she is the one who put the red nose in, or if she got the first red nosed dogs from someone else, and then continued to breed it through.....i'm not sure....
as far as how them registered dogs acquired a red nose.......well i guess that a story for around the campfire......
your dog looks very typical of what she was producing