J.K.
This is exactly why I have a very comprehensive illness policy in my daycare contract. There is a difference between wiping a child's nose from a regular run of the mill cold (which is a reasonable expectation, and common illness that you have to deal with in childcare), and wiping a child's nose to the point that it detracts from the care of the other children in care. It is the FREQUENCY of the nose wiping that is the issue. Chances are that whether your child had a temperature or not, a cold that severe would also cause her not to feel well too.
It's very hard for parents to assess how a child is really feeling when they only see them for a little bit of time in the morning. It's not uncommon for a child to feel generally ok in the morning for a couple of hours and then to poop out midday, from yes, just a common cold. It's also not uncommon for a child to come with parents saying " oh they have a little runny nose" and then after active play and a few hours of being up and around their nose is running like a faucet. Again, colds are part of life and it's almost impossible to stop the spread of them in childcare. If you sent home every child with a cold, you'd never have any clients. In my daycare, kids have to be well enough to play. Whether they have a fever or not, if they are too fatigued to play and all they can do is lay down or be held, they need to be with Mom or Dad, not in childcare.
I think that your reaction is out of line. We don't know the context or tone that was used by your care provider, so maybe that's what caused such a strong reaction. But just because she made this statement doesn't mean that she's not taking excellent care of your child in every other way. Unless you have other issues with her, this one thing shouldn't be a reflection of how you think she cares for your child.
Your provider didn't say she would no longer keep your daughter. She said if her nose gets any worse she won't be able to come to care... assuming just until her cold gets better. She's sick she needs to be home. You are in breach of contact for not giving adequate notice for withdrawal, and yeah... you owe her the $720.00, and probably an apology.
After reading your SWH it seems apparent that you had other issues with your childcare provider and this was just the tip of the iceberg. It doesn't sound like the communication either way was that great though... Your provider was SWEARING at you?? Good grief. And it's no wonder that daycare gets a bad rap. Well, good for you for finding another place. It's unfortunate that there are bad daycares and lazy providers out there. Just remember that there are good ones too... like the first provider you mentioned. Do your homework, ask lots of questions, be attentive and stay in good communication with your next provider. Good luck!