This poem is indeed about her mother, she is comparing her to the moon something beautiful, but also very cold and that sometimes makes us think of death. 'The rival' is her mother who captured her fathers attention and now seems to be always in between her and her husband, always arround. She describes her as if she were cold. Always wanting to say the last word, always wanting to get everyones attention 'great light borrowers'. She is impatient, always dissaproving her daughter, always showing disatisfaction, but at the same time, taking care of her in an inocent way, not leaving her alone and writing or calling to check on her from the States to England (where Plath was living at the moment of writing this poem) . Plath she doesn't seem to like this attention, she just wants to live her life without anyone telling her how to or without her mother being always there, in between saying the last word.
This is whati understand from this poem...i hope it helps you.