If the family had been open, honest and cooperative then I would give my loyalty to them or at least give a good amount of notice (2 months) about needing to fill their spot with a full-time child.

BUT...this family, sadly, does not seem to respect you, or at least has a great deal of difficulty keeping their lines of communication open and are not working WITH you so I would give notice and fill their spot with a full-time, cooperative, respectful family. I'm pretty sure I would have ended the contract with them some time ago due to their lack of communication.