I dont know actually. You would think that she'll carry a copy of the recessive lavender gene, but I'm not sure. I kept my white chick only because she was SUCH a nice baby. If I dont use her for showing she'll just be a pet.
Blue to Blue mating give equal numbers of Blue and Splash chicks. Splash is white with odd blue feathers. This most likely what you have.
To get recessive White, both coloured parents must carry the gene.
No reason why you can't breed with it.
You have no reason to be shocked, just brush up on a bit of poultry genetics, " knowledge is a light burden to carry".