I agree that you didn't do a thing wrong, and acted fine. Your reaction was human, and you stood up for yourself, which is great. You didn't abandon your brother, he was at his father's house! He was fine. I think it's more helpful to him in the long run to not put up with rude behavior from him. Sorry your mother didn't see it that way. Clearly she doesn't have a good baseline in the first place so it's no wonder she found the situation wrong.

Would you mind telling us how Amy/Amelia is doing??