Sometimes with a problem family once you create a letter to them stating this is what is not working and if there is no improvement by XXX date then you will be receiving your termination papers since this relationship is not working out for child, caregiver and other children in care. If you want to push the point home you could add something to the effect that I can not let the actions of one family spoil the daycare experience for all other families.

This lets the family know they are the only ones causing major issues and gives them a timeline for shaping up or being shipped out. At least the family will have no one to blame if they are terminated but themselves in the sense that you gave them the list of requirements and time to make the changes.