Both ESA and nobody's the A.

First from you. How do you perceive her motivation for what she did? Do you think she did what she did because she maliciously hates you and your daughter? Or can you see she was concerned and from HER point of view she didn't want any harm to come to your daughter because she loves you guys? It looks to me she did what she did with good intentions. Yes from your point of view it was wrong but it was not out of bad intention.

She made a mistake by disciplining your daughter in a situation she should have had no part of but she is human and you hopefully can forgive her.

You made a mistake by kicking her out of your house, but you are human and she can hopefully forgive you. What you did was to protect your family who you Love and you did so with good intentions

You both were wrong but it doesn't matter nobody wins or loses at life, nobody keeps a score, nobody is perfect. Find it in yourself to see her good intentions and ask she see your good intentions and move on. Conflict happens but a good friendship should not be ruined because of bad communication.