Even if you don't do it, you could discuss it with her. How do you think it will make you feel if you do it? Is it that feeling that you want to get that motivates you to do this? Or are you wanting to share something special from your childhood with T? Use this as a technique to help you cry? What? It's interesting!
I have never sung to my T (and don't want to). My T, though, has sung to me several time--just a few lines from a song here and there. He has a really nice voice and sings in a vocal group. I never felt pressure to reciprocate, thank goodness.

(My singing voice is not good.)