I think it is really hard to separate our feelings towards the parents from those towards the child. While the child's behaviour may not match your contract termination terms, the payment issues do and you should keep to your word of 'this is the last chance'. They will continue to take advantage of your kindness.

Your issues with the parents probably magnify your issues with the child so that annoying behaviours seem more so than they would with a family you liked better! Either way, the issues are there and will most likely get more annoying if the parents continue with their current ways!