I want to just repeat what every one else here has said...I'm so sorry your little one had to experience that!
However...my first thoughts when I saw the photo of the raw area was an "allergic reaction" to the adhesive on the tape used to secure the bandage.
That is exactly what that looks like on a human patient who comes in contact with an allergic agent in the "tape".
So, before jumping to conclusions about the Vet's skills...it IS possible that this is something that your Yorkie just happens to be allergic to.
I would definitely make sure this is known to any future Vet's you may go to and make sure it's documented in the medical records to prevent this from occurring again especially after any future surgeries.
Again...to me, it looks like a severe allergic reaction to the "tape".