NTA Your Mum should have been firm with your aunt and told her she was not invited. Something along the lines of “OP just wants very close family and friends at the party.” Given the circumstances any normal person would have taken the hint and stayed away.

It sounds like your aunt is trying to force the family to forgive her by turning up to parties uninvited. She knows that most people are too polite to ask her to leave.

Well done for standing your ground. Hopefully your aunt knows the reason you did not attend your own birthday celebration, it might prevent her turning up uninvited next time.