I tell parents if their child is sick enough to need Tylenol, they are too sick for daycare. I had a parent who wanted me to medicate their children, and I finally got to the point that enough was enough. If I were you, I would start trying to find another family to replace this one with. Then, once you have someone lined up, (or before if mom keeps this mess up) go ahead and give mom notice. You are not responsible for her job. As the parent, she is responsible for giving correct dosages for medications (or not sending them at all), for caring for her sick child, and for respecting her child care provider.
This is a hard job, but is 100% better with really good families who respect the work you do. Trust me - I was there with you just a few short weeks ago. I have a new family who took the place of the family that was making my life miserable, and it is totally a night and day difference!
Feel free to vent with us too. That always helps me, and helps me not feel so alone in this job. Have a wonderful day!!