I recently went through a similiar situation with a family that also refused to pay their two weeks notice. They told me that if I took them to court to collect fees or sent them to a collection agency they would call and file a complaint on me. In California a complaint stays on your record even if it is unfounded. I just let it go, it wasn't worth it to me to have any kind of complaint on my license.
I have never required a two week deposit until this situation. My new family I enrolled have paid a 2 week deposit that I put in savings. I will always require a 2 week deposit from now on, even if they have to make it in payments.