DO they pay before or after care has taken place? Have they paid for those 3 days but owe you for the following 2 weeks?
If they have been trouble for a while and are not working with you, following terms in the contract then I would lean to filling the spot with a family that is willing to work with you, follow terms and pay your current going rate. The only catch is since they are not causing harm or harassing you or anything serious then I would lean to following your contract policy for letting a family go...which may be giving 2 weeks notice or such.
You've been sick and exhausted and you are not being respected but try to clear all that from your mind when making your decision. Just dropping them today or in 3 days may not be the best move. Ideally you'll follow your own contracted policy so the family has less ability to ruin your reputation.