I just posted on another thread a few minutes ago that I made a rule for myself in my first year in business that if the parents work with me no matter what the issue I will continue to try and try. I tell families this at the interview stage. I learned the hard way as you are learning right now that if the parents don't help you that it is a lost cause.
Children need consistency at home and at daycare with rules, food and sleep expectations and we have to be a TEAM! Period.
You listed a whole lot of problems in your original post and you already addressed all the issues with the parent who is also giving you grief. I agree with the poster that said - close your eyes and imagine your stress-free days without this family. Advertise - interview - NOW! Good luck.