Sarcoptic mange can be spread to humans in that the mange mites can and will bite people. However, they CANNOT live and breed on people.
Islandgirl82, as far as ease of treatment, sarcoptic mange is actually quite easy to treat once you know that's what it is. Many topical flea treatments...
Ultimately you may NEVER be able to leave her with chickens unsupervised. She is a mix of two breeds that can have a VERY high prey drive (not really ideal as flock guardians, though it can work with the right dog). I own two German Shepherds and a Border Collie, and oddly, the Border Collie...