It's the perfect way to answer. It explains the facts of the garment, your feelings of the covenants behind the garment and you didn't reveal anything that you shouldn't.
I'm glad to hear that your mother is more accepting.
I say that we need to teach our people to find their answers in the scriptures...But the unfortunate thing is that so many of us are not reading the scriptures. We do not know what is in them, and therefore we speculate about things that we ought to have found in the scriptures themselves. I think that therein is one of our biggest dangers of today."
--President Harold B. Lee, December, 1972