People often don't realize that it's OK to change our mind. Sometimes, changing our mind is a matter of pride getting in the way of common sense.
My W told me she would do a number of things for me. On things I didn't remind her of, she didn't do. On things that I reminded her of, she changed her mind.
Only ask about the singing lessons if you truly want to learn to and has nothing to do with spending time with your W and hoping it will bring the two of you closer.
Remember, your W is asking for space.
Try the indirect route. Ask your W who she might know that could give you singing lessons. Wait for her to respond with either a suggestion or two, or to offer herself. If she offers herself, the ask her to firm a date. Have no expectations over this.
If she makes other suggestions, then it would be in your best interest to follow those suggestions up. Otherwise, she will see it as some tactic. And it probably would be.
