"From you, her mother, and so kind, so indulgent a mother, the question could not give offence. It would be the natural result of your affection for her. She used to be all unreserve, and to you more especially."

I think Elinor is pointing out to her mother that they both have especially been unreserved with each other, and she has been very indulgent towards her daughter in this case of Willoughby, and so the best person to ask this intimate question.