Betadine really isn't what you want for mites... What you want is Provent a Mite.

You should soak him in warm water with a drop of dawn dish soap. This will help remove the mites, and the PAM will kill them.

You shouldn't take your snakes to the vet if they have mites as you could spread them.

Mites are a very serious issue, and can even kill your snake if not taken care of.