
You'ere not going to like this, but a restitch because the bitch had been allowed to get to her wound isn't the vet's fault, so not their responsibility to cover the cost of repair.
Regarding the surgery itself, there are many methods of stitching wounds, whether that's individual external stitches, one long sub-cut stitch and tissue glue, or whatever, and each vet will have their preference - none is more 'right' than any other.