Wow. I simply cannot imagine what your teen self felt at that time. Hugs.
No, I would not get over this and I would stand my ground. This woman would not be invited to my birthday party and quite frankly, I would not care who knew why or not. I would not go out of my way to tell anyone, but if it came up, I would not just sit back and say nothing either.
Not only did she react badly to the situation, but she never apologized for her reaction either. She clearly feels she did nothing wrong.
Stamd your ground. Woman is not invited, period. If she is there, I don't know that I would leave right away, (because clearly everyone else invited seems to be people you do care about and might not know the situation), but I would not be there long, and suddenly, I would feel sick. And mom would be told in no un-cerain terms that I hope she thinks it was worth it inviting this person. Because she just destroyed the relationship that you and she have. I would not be talking to my mother for a long, long time.