Some people would be better fitted in jobs with no patient/people/living being contact at all, the same goes for human doctors as well.
They are so full of themselves, there is no room left for empathy or interest in the matter nor the patients at all.
Massage your dogs ears for me for being...
What an awful experience to have at the vet clinic! :hugs
Adding antibiotics to the treatment sounds sensible to me as often the skin is infected by bacteria due to the continuous scratching, and the prednisone will help with the itching..
I hope that your dog will heal soon and at least have...
With kids and other dogs in the family, I strongly advise to treat all the dogs at the same time when suspecting mange or the circle never really stops as it is highly contageous.
With 3 injections each 9-10 days apart the infection will be covered and you can wash the dogs without any problems.