I would give them a two week notice. Keep it short and sweet.

Mr. and Mrs. Whatever,

Please consider this my two week notice. I can work for you until 10/10/2014.

Sincerely,
Rayne Selene

Don't add any reasons to your written notice (and save a copy for yourself). If they ask, just tell them that you feel it isn't a good fit. Don't go into details. They will probably be angry and won't take anything you say to heart, so don't waste your breath.

I'm assuming you don't need the job, so if you do, maybe give quitting a second thought -- but this sounds like a really terrible situation. The kid attacks you and the parents can't say no? The mother sounds very difficult.

They probably gave you that spiel about wanting someone to stay long term because they can't get anyone to stay more than a month