So sorry about your dog being sick and for your frustration. I am sure your dog appreciates that you are so understanding.
I had an old cat who used to throw up on my light colored living room carpet twice a day, every day for 6 months. As soon as this started, I took him to the vet time after time and had many tests done but they could never find anything wrong.
I used to beg him to please throw up on the tile instead, but he insisted on the living room carpet. I know that feeling of wanting to scream. I was always very sweet to him, and told him that I understood, but it drove me crazy!