[RHSeeger]

They two different questions. One is asking if you are you able to, the other if you are willing to. I don't teach my daughter to correct people outside the house, but I do want her to speak properly when out there.

It's the same as everyone knows what she means when she says "libary", but I correct her to pronounce it "library".

[taejo]

Pragmatically, neither of them is a question: they are more and less polite requests (or a request and an order). Your daughter is perceptive enough to have worked this out; probably you did too, but at some point decided to override your unconcious competence with concious nitpicking.