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Martha appears to be bipolar and it was mentally exhausting for Violet to raise her. Martha is 23, but still lives with mother continuing her abuse when she is in a severe mood episode. Violet gave up her career as a singer for her, getting nothing in return. Yet, externally she appears to be calm. She dutifully continues to carry her cross despite Martha's abuse. . Lila has her own mother/daughter story as the movie progresses that also centers around song writing and singing. Violet and Lila come together and transform each other. Even though transformation was short lived for Violet, she fulfilled her dreams.

I personally don't see any plot holes. What happened to amnesia? Amnesia could reverse on its own. But I believe it was not amnesia that prevented Lila from singing. It was her guilt. I recommend you to watch this movie. Your perception could be different.