A Quokka Dreeds its Weird

I suggest duct-taping the dog's legs together and muzzle shut. Then attach the parakeet to the dog's nose the same way it was attached to your hand.

Teach the dog that the parakeet is not a toy, especially not a chew toy. But the dog can be, if he can't learn to behave.

Edit: If it's not perfectly obvious, this suggestion is pretty much tongue in cheek; I don't condone animal abuse. But you sound awfully exasperated.