I have to agree with Tirned Tinnu. I never really saw Galadriel as a mother figure for Frodo. I think Frodo was no less cautious of her than the 'big folk' he travelled with (Gandalf excepted). He does not offer the ring to her out of the love a son gives his mother. She does not really inspire that love in him (although I'm less sure in Sam's case).
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The inimical is often more instructive than the benign. Between screams, try to pay attention.
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