I don't even know where to start.....
Telling you to f-off?? Psychological issues (pulling own hair, causing herself to vomit, and MOM IS AFRAID TO SLEEP?????)? Mom consistently flouting the daycare rules, not to mention generally disrespecting.
I hope you have already written that termination notice, because you know that's what you need to do. If you can't do it for yourself, do it for your kids and the other daycare kids. It's not fair to them to have these little devil minions in their environment!!!
Best of luck!